@unpublished{KapanadzeSchulze2001,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Symbolic calculus for boundary value problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26046},
  year      = {2001},
  abstract  = {Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy of symbols. The symbol structure is responsible or ellipicity and for the nature of parametrices within an algebra of "edge-degenerate" pseudo-differential operators. The edge symbol component of that hierarchy takes values in boundary value problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in this theory, in particular, the contribution with holomorphic operatot-valued Mellin symbols. We establish a calculus in s framework of "twisted homogenity" that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces. We then derive an equivalent representation with a particularly transparent composition behaviour.},
  language  = {en}
}
@unpublished{ManicciaMughetti2001,
  author    = {Maniccia, L. and Mughetti, M.},
  title     = {Weyl calculus for a class of subelliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26038},
  year      = {2001},
  abstract  = {Weyl-H{\"o}rmander calculus is used to get a parametrix in OPS¹-m sub(½, ½)(Ω)for a class of subelliptic pseudodifferential operators in OPS up(m)sub(1, 0)(Ω) with real non-negative principal symbol.},
  language  = {en}
}
@unpublished{YihongLi2001,
  author    = {Yihong, Du and Li, Ma},
  title     = {Some remarks related to De Giorgi's conjecture},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26027},
  year      = {2001},
  abstract  = {For several classes of functions including the special case f(u) = u - u³, we obtain boundedness and symmetry results for solutions of the problem -Δu = f(u) defined on R up(n). Our results complement a number of recent results related to a conjecture of De Giorgi.},
  language  = {en}
}
@unpublished{MaXu2001,
  author    = {Ma, Li and Xu, Xingwang},
  title     = {Positive solutions of a logistic equation on unbounded intervals},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26015},
  year      = {2001},
  abstract  = {In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on R+ or on R. These equations are stationary versions of the Fisher equations and the KPP equations. We also study the blow up region of a sequence of the solutions when the parameter approachs a critical value and the nonexistence of positive solutions beyond the critical value. We use the direct method and the sub and super solution method.},
  language  = {en}
}
@unpublished{KrainerSchulze2001,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 3: Chapter 6+7]},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26000},
  year      = {2001},
  abstract  = {We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is specifically designed to contain both the classical systems of parabolic equations of general form and their inverses, parabolicity being reflected purely on symbolic level. To this end, we assign t = ∞ the meaning of an anisotropic conical point, and prove that this interprtation is consistent with the natural setting in the analysis of parabolic PDE. Hence, major parts of this work consist of the construction of an appropriate anisotropiccone calculus of so-called Volterra operators. In particular, which is the most important aspect, we obtain the complete characterization of the microlocal and the global kernel structure of the inverse of parabolicsystems in an infinite space-time cylinder. Moreover, we obtain perturbation results for parabolic equations from the investigation of the ideal structure of the calculus.},
  language  = {en}
}
@unpublished{KrainerSchulze2001,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 2: Chapter 3-5]},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25992},
  year      = {2001},
  abstract  = {We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is specifically designed to contain both the classical systems of parabolic equations of general form and their inverses, parabolicity being reflected purely on symbolic level. To this end, we assign t = ∞ the meaning of an anisotropic conical point, and prove that this interprtation is consistent with the natural setting in the analysis of parabolic PDE. Hence, major parts of this work consist of the construction of an appropriate anisotropiccone calculus of so-called Volterra operators. In particular, which is the most important aspect, we obtain the complete characterization of the microlocal and the global kernel structure of the inverse of parabolicsystems in an infinite space-time cylinder. Moreover, we obtain perturbation results for parabolic equations from the investigation of the ideal structure of the calculus.},
  language  = {en}
}
@unpublished{KrainerSchulze2001,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 1: Chapter 1+2]},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25987},
  year      = {2001},
  abstract  = {We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is specifically designed to contain both the classical systems of parabolic equations of general form and their inverses, parabolicity being reflected purely on symbolic level. To this end, we assign t = ∞ the meaning of an anisotropic conical point, and prove that this interprtation is consistent with the natural setting in the analysis of parabolic PDE. Hence, major parts of this work consist of the construction of an appropriate anisotropiccone calculus of so-called Volterra operators. In particular, which is the most important aspect, we obtain the complete characterization of the microlocal and the global kernel structure of the inverse of parabolicsystems in an infinite space-time cylinder. Moreover, we obtain perturbation results for parabolic equations from the investigation of the ideal structure of the calculus.},
  language  = {en}
}
@unpublished{KytmanovMyslivetsSchulzeetal.2001,
  author    = {Kytmanov, Aleksandr and Myslivets, Simona and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Elliptic problems for the Dolbeault complex},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25979},
  year      = {2001},
  abstract  = {The inhomogeneous ∂-equations is an inexhaustible source of locally unsolvable equations, subelliptic estimates and other phenomena in partial differential equations. Loosely speaking, for the anaysis on complex manifolds with boundary nonelliptic problems are typical rather than elliptic ones. Using explicit integral representations we assign a Fredholm complex to the Dolbeault complex over an arbitrary bounded domain in C up(n).},
  language  = {en}
}
@unpublished{CoriascoSchroheSeiler2001,
  author    = {Coriasco, Sandro and Schrohe, Elmar and Seiler, J{\"o}rg},
  title     = {Bounded imaginary powers of differential operators on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25962},
  year      = {2001},
  abstract  = {We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B,1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers A up(z), z ∈ C. We also obtain sufficient information on the resolvent of A to show the boundedness of the pure imaginary powers. Examples concern unique solvability and maximal regularity of the solution of the Cauchy problem u' - Δu = f, u(0) = 0, for the Laplacian on conical manifolds.},
  language  = {en}
}
@unpublished{SchulzeSeiler2001,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {The edge algebra structure of boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25955},
  year      = {2001},
  abstract  = {Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols.},
  language  = {en}
}
@unpublished{Schulze2001,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Operators with symbol hierarchies and iterated asymptotics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25948},
  year      = {2001},
  abstract  = {Contents: Introduction 1 Edge calculus with parameters 1.1 Cone asymptotics and Green symbols 1.2 Mellin edge symbols 1.3 The edge symbol algebra 1.4 Operators on a manifold with edges 2 Corner symbols and iterated asymptotics 2.1 Holomorphic corner symbols 2.2 Meromorphic corner symbols and ellipicity 2.3 Weighted corner Sobolev spaces 2.4 Iterated asymptotics 3 The edge corner algebra with trace and potential conditions 3.1 Green corner operators 3.2 Smoothing Mellin corner operators 3.3 The edge corner algebra 3.4 Ellipicity and regularity with asymptotics 3.5 Examples and remarks},
  language  = {en}
}
@unpublished{EgorovKondratievSchulze2001,
  author    = {Egorov, Yu. and Kondratiev, V. and Schulze, Bert-Wolfgang},
  title     = {On completeness of eigenfunctions of an elliptic operator on a manifold with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25937},
  year      = {2001},
  abstract  = {Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Completeness of root functions},
  language  = {en}
}
@unpublished{Korey2001,
  author    = {Korey, Michael Brian},
  title     = {A decomposition of functions with vanishing mean oscillation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25929},
  year      = {2001},
  abstract  = {A function has vanishing mean oscillation (VMO) on R up(n) if its mean oscillation - the local average of its pointwise deviation from its mean value - both is uniformly bounded over all cubes within R up(n) and converges to zero with the volume of the cube. The more restrictive class of functions with vanishing lower oscillation (VLO) arises when the mean value is replaced by the minimum value in this definition. It is shown here that each VMO function is the difference of two functions in VLO.},
  language  = {en}
}
@unpublished{XiaochunWitt2001,
  author    = {Xiaochun, Liu and Witt, Ingo},
  title     = {Asymptotic expansions for bounded solutions to semilinear Fuchsian equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25912},
  year      = {2001},
  abstract  = {It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.},
  language  = {en}
}
@unpublished{CoriascoPanarese2000,
  author    = {Coriasco, Sandro and Panarese, Paolo},
  title     = {Fourier integral operators defined by classical symbols with exit behaviour},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25896},
  year      = {2000},
  abstract  = {We continue the investigation of the calculus of Fourier Integral Operators (FIOs) in the class of symbols with exit behaviour (SG symbols). Here we analyse what happens when one restricts the choice of amplitude and phase functions to the subclass of the classical SG symbols. It turns out that the main composition theorem, obtained in the environment of general SG classes, has a "classical" counterpart. As an application, we study the Cauchy problem for classical hyperbolic operators of order (1, 1); for such operators we refine the known results about the analogous problem for general SG hyperbolic operators. The material contained here will be used in a forthcoming paper to obtain a Weyl formula for a class of operators defined on manifolds with cylindrical ends, improving the results obtained in [9].},
  language  = {en}
}
@unpublished{Tepoyan2000,
  author    = {Tepoyan, Liparit},
  title     = {Degenerated operator equations of higher order},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25888},
  year      = {2000},
  abstract  = {Content: 1 Introduction 2 The one-dimensional case 2.1 The space Wm sub (α) 2.2 Self-adjoint Equation 2.3 Non-selfadjoint Equation 3 Operator Equation},
  language  = {en}
}
@unpublished{NazaikinskiiSternin2000,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {On surgery in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25873},
  year      = {2000},
  abstract  = {We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.},
  language  = {en}
}
@unpublished{SavinSternin2000,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Eta invariant and parity conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25869},
  year      = {2000},
  abstract  = {We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 11: Noncommutative analysis and high-frequency asymptotics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25857},
  year      = {2000},
  abstract  = {Content: Chapter 11: Noncommutative Analysis and High-Frequency Asymptotics 11.1 Statement of the Problem 11.2 Mixed Asymptotics: the General Scheme 11.3 The Asymptotic Solution of Main Problem 11.4 Analysis of the Asymptotic Solution},
  language  = {en}
}
@unpublished{RabinovichSchulzeTarkhanov2000,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {C*-algebras of ISO's with oscillating symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25847},
  year      = {2000},
  abstract  = {For a domain D subset of IRn with singular points on the boundary and a weight function ω infinitely differentiable away from the singularpoints in D, we consider a C*-algebra G (D; ω) of operators acting in the weighted space L² (D, ω). It is generated by the operators XD F-¹ σ F XD where σ is a homogeneous function. We show that the techniques of limit operators apply to define a symbol algebra for G (D; ω). When combined with the local principle, this leads to describing the Fredholm operators in G (D; ω).},
  language  = {en}
}
@unpublished{KytmanovMyslivetsTarkhanov2000,
  author    = {Kytmanov, Aleksandr and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Removable singularities of CR functions on singular boundaries},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25836},
  year      = {2000},
  abstract  = {The problem of analytic representation of integrable CR functions on hypersurfaces with singularities is treated. The nature o singularities does not matter while the set of singularities has surface measure zero. For simple singularities like cuspidal points, edges, corners, etc., also the behaviour of representing analytic functions near singular points is studied.},
  language  = {en}
}
@unpublished{KrainerSchulze2000,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {Long-time asymptotics with geometric singularities in the spatial variables},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25824},
  year      = {2000},
  abstract  = {Content: Introduction 1 Anisotropic operators in a cylinder with a conical base 1.1 Manifolds with conical singularities and opertors of Fuchs type 1.2 Typical operators and symbol structures 2 Weighted wedge Sobolev spaces and edge asymptotics 2.1 Discrete edge asymptotics 2.2 Continuos edge asymptotics with discrete limit at infinity 2.3 Calculus with operator valued symbols 3 Corner asymptotics at infinity 3.1 The structure of singular functions 3.2 Operators with trace and potential conditions 3.3 Asymptotics and (anisotropic) elliptic regularity},
  language  = {en}
}
@unpublished{Rozenblum2000,
  author    = {Rozenblum, G.},
  title     = {On some analytical index formulas related to operator-valued symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25811},
  year      = {2000},
  abstract  = {For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that uasual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 3: Applications of noncommutative analysis to operator algebras on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25801},
  year      = {2000},
  abstract  = {Content: Chapter 3: Applications of Noncommutative Analysis to Operator Algebras on Singular Manifolds 3.1 Statement of the problem 3.2 Operators on the Model Cone 3.3 Operators on the Model Cusp of Order k 3.4 An Application to the Construction of Regularizers and Proof of the Finiteness Theorem},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 2: Exactly soluble commutation relations (The simplest class of classical mechanics)},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25796},
  year      = {2000},
  abstract  = {Content: Chapter 2: Exactly SolubleCommutation Relations (The Simplest Class of Classical Mechanics) 2.1 Some examples 2.2 Lie commutation relations 2.3 Non-Lie (nonlinear) commutation relations},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Pseudodifferential operators on manifolds with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25783},
  year      = {2000},
  abstract  = {We describe an algebra of pseudodifferential operators on a manifold with corners.},
  language  = {en}
}
@unpublished{SchulzeShlapunovTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Green integrals on manifolds with cracks},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25777},
  year      = {2000},
  abstract  = {We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Part II: Quantization by the method of ordered operators (Noncommutative Analysis) : Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25762},
  year      = {2000},
  abstract  = {Content: 0.1 Preliminary Remarks Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems 1.1 Functions of One Operator (Functional Calculi) 1.2 Functions of Several Operators 1.3 Main Formulas of Operator Calculus 1.4 Main Tools of Noncommutative Analysis 1.5 Composition Laws and Ordered Representations},
  language  = {en}
}
@unpublished{KapanadzeSchulze2000,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential crack theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25759},
  year      = {2000},
  abstract  = {Crack problems are regarded as elements in a pseudo-differential algbra, where the two sdes int S± of the crack S are treated as interior boundaries and the boundary Y of the crack as an edge singularity. We employ the pseudo-differential calculus of boundary value problems with the transmission property near int S± and the edge pseudo-differential calculus (in a variant with Douglis-Nirenberg orders) to construct parametrices od elliptic crack problems (with extra trace and potential conditions along Y) and to characterise asymptotics of solutions near Y (expressed in the framework of continuous asymptotics). Our operator algebra with boundary and edge symbols contains new weight and order conventions that are necessary also for the more general calculus on manifolds with boundary and edges.},
  language  = {en}
}
@unpublished{SavinSternin2000,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Eta-invariant and Pontrjagin duality in K-theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25747},
  year      = {2000},
  abstract  = {The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.},
  language  = {en}
}
@unpublished{Myslivets2000,
  author    = {Myslivets, Simona},
  title     = {On the boundary behaviour of the logarithmic residue integral},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25733},
  year      = {2000},
  abstract  = {A formula of multidimensional logarithmic residue is proved for holomorphic maps with zeroes on the boundary of a bounded domain in Cn.},
  language  = {en}
}
@unpublished{KapanadzeSchulze2000,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Boundary value problems on manifolds with exits to infinity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25727},
  year      = {2000},
  abstract  = {We construct a new calculus of boundary value problems with the transmission property on a non-compact smooth manifold with boundary and conical exits to infinity. The symbols are classical both in covariables and variables. The operators are determined by principal symbol tuples modulo operators of lower orders and weights (such remainders are compact in weighted Sobolev spaces). We develop the concept of ellipticity, construct parametrices within the algebra and obtain the Fredholm property. For the existence of Shapiro-Lopatinskij elliptic boundary conditions to a given elliptic operator we prove an analogue of the Atiyah-Bott condition.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotics of solutions to elliptic equatons on manifolds with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25716},
  year      = {2000},
  abstract  = {We show an explicit link between the nature of a singular point and behaviour of the coefficients of the equation, under which formal asymptotic expansions are still available.},
  language  = {en}
}
@unpublished{SavinSchulzeSternin2000,
  author    = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic operators in subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25701},
  year      = {2000},
  abstract  = {We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.},
  language  = {en}
}
@unpublished{Schrohe2000,
  author    = {Schrohe, Elmar},
  title     = {A short introduction to Boutet de Monvel's calculus},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25696},
  year      = {2000},
  abstract  = {This paper provides an introduction to Boutet de Monvel's calculus on the half-space IRn (positiv) in the framework of a pseudodifferential calculus with operator-valued symbols.},
  language  = {en}
}
@unpublished{Shlapunov2000,
  author    = {Shlapunov, Alexander},
  title     = {On Iterations of double layer potentials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25687},
  year      = {2000},
  abstract  = {We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.},
  language  = {en}
}
@unpublished{KapanadzeSchulzeWitt2000,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang and Witt, Ingo},
  title     = {Coordinate invariance of the cone algebra with asymptotics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25671},
  year      = {2000},
  abstract  = {The cone algebra with discrete asymptotics on a manifold with conical singularities is shown to be invariant under natural coordinate changes, where the symbol structure (i.e., the Fuchsian interior symbol, conormal symbols of all orders) follows a corresponding transformation rule.},
  language  = {en}
}
@unpublished{Sadykov1999,
  author    = {Sadykov, Timour},
  title     = {Hypergeometric systems of differential equations and amoebas of rational functions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25665},
  year      = {1999},
  abstract  = {We study the approach to the theory of hypergeometric functions in several variables via a generalization of the Horn system of differential equations. A formula for the dimension of its solution space is given. Using this formula we construct an explicit basis in the space of holomorphic solutions to the generalized Horn system under some assumptions on its parameters. These results are applied to the problem of describing the complement of the amoeba of a rational function, which was posed in [12].},
  language  = {en}
}
@unpublished{Fedosov1999,
  author    = {Fedosov, Boris},
  title     = {Pseudo-differential operators and deformation quantization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25651},
  year      = {1999},
  abstract  = {Using the Riemannian connection on a compact manifold X, we show that the algebra of classical pseudo-differential operators on X generates a canonical deformation quantization on the cotangent manifold T*X. The corresponding Abelian connection is calculated explicitly in terms of the of the exponential mapping. We prove also that the index theorem for elliptic operators may be obtained as a consequence of the index theorem for deformation quantization.},
  language  = {en}
}
@unpublished{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Operator algebras with symbol hierarchies on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25647},
  year      = {1999},
  abstract  = {Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.},
  language  = {en}
}
@unpublished{KytmanovMyslivetsTarkhanov1999,
  author    = {Kytmanov, Alexander and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic representation of CR Functions on hypersurfaces with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25631},
  year      = {1999},
  abstract  = {We prove a theorem on analytic representation of integrable CR functions on hypersurfaces with singular points. Moreover, the behaviour of representing analytic functions near singular points is investigated. We are aimed at explaining the new effect caused by the presence of a singularity rather than at treating the problem in full generality.},
  language  = {en}
}
@unpublished{SchroheSeiler1999,
  author    = {Schrohe, Elmar and Seiler, J{\"o}rg},
  title     = {Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25621},
  year      = {1999},
  abstract  = {Given a manifold B with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale of Lp-Sobolev spaces. Ellipticity is proven to be equivalent to the Fredholm property in these spaces, it turns out to be independent of the choice of p. We then show that the cone algebra is closed under inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to analyze the behaviour of these operators on Lp(B).},
  language  = {en}
}
@unpublished{LauterSeiler1999,
  author    = {Lauter, Robert and Seiler, J{\"o}rg},
  title     = {Pseudodifferential analysis on manifolds with boundary - a comparison of b-calculus and cone algebra},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25611},
  year      = {1999},
  abstract  = {We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose's (overblown) b-calculus and Schulze's cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.},
  language  = {en}
}
@unpublished{Duduchava1999,
  author    = {Duduchava, Roland},
  title     = {The Green formula and layer potentials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25601},
  year      = {1999},
  abstract  = {The Green formula is proved for boundary value problems (BVPs), when "basic" operator is arbitrary partial differential operator with variable matrix coefficients and "boundary" operators are quasi-normal with vector-coeficients. If the system possesses the fundamental solution, representation formula for a solution is derived and boundedness properties of participating layer potentials from function spaces on the boundary (Besov, Zygmund spaces) into appropriate weighted function spaces on the inner and the outer domains are established. Some related problems are discussed in conclusion: traces of functions from weighted spaces, traces of potential-type functions, Plemelji formulae,Calder{\´o}n projections, restricted smoothness of the underlying surface and coefficients. The results have essential applications in investigations of BVPs by the potential method, in apriori estimates and in asymptotics of solutions.},
  language  = {en}
}
@unpublished{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25596},
  year      = {1999},
  abstract  = {We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin1999,
  author    = {Nazaikinskii, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25582},
  year      = {1999},
  abstract  = {In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSternin1999,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir E. and Sternin, Boris},
  title     = {On the homotopy classification of elliptic operators on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25574},
  year      = {1999},
  abstract  = {We study the homotopy classification of elliptic operators on manifolds with singularities and establish necessary and sufficient conditions under which the classification splits into terms corresponding to the principal symbol and the conormal symbol.},
  language  = {en}
}
@unpublished{SchulzeSterninSavin1999,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Savin, Anton},
  title     = {The homotopy classification and the index of boundary value problems for general elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25568},
  year      = {1999},
  abstract  = {We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.},
  language  = {en}
}
@unpublished{RabinovichSchulzeTarkhanov1999,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems in domains with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25552},
  year      = {1999},
  abstract  = {We describe Fredholm boundary value problems for differential equations in domains with intersecting cuspidal edges on the boundary.},
  language  = {en}
}
@unpublished{AizenbergTarkhanov1999,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Bohr phenomenon for elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25547},
  year      = {1999},
  abstract  = {In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.},
  language  = {en}
}
@unpublished{NazaikinskiiSternin1999,
  author    = {Nazaikinskii, Vladimir E. and Sternin, Boris},
  title     = {Surgery and the relative index in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25538},
  year      = {1999},
  abstract  = {We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1999,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A general index formula on tropic manifolds with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501},
  year      = {1999},
  abstract  = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.},
  language  = {en}
}
@unpublished{SchulzeSavinSternin1999,
  author    = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris},
  title     = {Elliptic operators in subspaces and the eta invariant},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25496},
  year      = {1999},
  abstract  = {The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.},
  language  = {en}
}
@unpublished{Schrohe1999,
  author    = {Schrohe, Elmar},
  title     = {Noncommutative residues, Dixmier's Trace, and heat trace expansions on manifolds with boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25486},
  year      = {1999},
  abstract  = {For manifolds with boundary, we define an extension of Wodzicki's noncommutative residue to boundary value problems in Boutet de Monvel's calculus. We show that this residue can be recovered with the help of heat kernel expansions and explore its relation to Dixmier's trace.},
  language  = {en}
}
@unpublished{SavinSternin1999,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Elliptic operators in odd subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25478},
  year      = {1999},
  abstract  = {An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.},
  language  = {en}
}
@unpublished{SavinSternin1999,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Elliptic operators in even subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25461},
  year      = {1999},
  abstract  = {An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.},
  language  = {en}
}
@unpublished{SchulzeShlapunovTarkhanov1999,
  author    = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Regularisation of mixed boundary problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25454},
  year      = {1999},
  abstract  = {We show an application of the spectral theorem in constructing approximate solutions of mixed boundary value problems for elliptic equations.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin1999,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization and the wave packet transform},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25447},
  year      = {1999},
  language  = {en}
}
@unpublished{SchroheSchulze1999,
  author    = {Schrohe, Elmar and Schulze, Bert-Wolfgang},
  title     = {Edge-degenerate boundary value problems on cones},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25436},
  year      = {1999},
  abstract  = {We consider edge-degenerate families of pseudodifferential boundary value problems on a semi-infinite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near infinity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.},
  language  = {en}
}
@unpublished{Witt1999,
  author    = {Witt, Ingo},
  title     = {On the factorization of meromorphic Mellin symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25427},
  year      = {1999},
  abstract  = {It is prooved that mermorphic, parameter-dependet elliptic Mellin symbols can be factorized in a particular way. The proof depends on the availability of logarithms of pseudodifferential operators. As a byproduct, we obtain a characterization of the group generated by pseudodifferential operators admitting a logarithm. The factorization has applications to the theory os pseudodifferential operators on spaces with conical singularities, e.g., to the index theory and the construction of various sub-calculi of the cone calculus.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1999,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Ellipticity and parametrices on manifolds with caspidal edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25411},
  year      = {1999},
  language  = {en}
}
@unpublished{Shlapunov1999,
  author    = {Shlapunov, Alexander},
  title     = {Iterations of self-adjoint operators and their applications to elliptic systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25401},
  year      = {1999},
  abstract  = {Let Hsub(0), Hsub(1) be Hilbert spaces and L : Hsub(0) -> Hsub(1) be a linear bounded operator with ||L|| ≤ 1. Then L*L is a bounded linear self-adjoint non-negative operator in the Hilbert space Hsub(0) and one can use the Neumann series ∑∞sub(v=0)(I - L*L)v L*f in order to study solvability of the operator equation Lu = f. In particular, applying this method to the ill-posed Cauchy problem for solutions to an elliptic system Pu = 0 of linear PDE's of order p with smooth coefficients we obtain solvability conditions and representation formulae for solutions of the problem in Hardy spaces whenever these solutions exist. For the Cauchy-Riemann system in C the summands of the Neumann series are iterations of the Cauchy type integral. We also obtain similar results 1) for the equation Pu = f in Sobolev spaces, 2) for the Dirichlet problem and 3) for the Neumann problem related to operator P*P if P is a homogeneous first order operator and its coefficients are constant. In these cases the representations involve sums of series whose terms are iterations of integro-differential operators, while the solvability conditions consist of convergence of the series together with trivial necessary conditions.},
  language  = {en}
}
@unpublished{Fedosov1998,
  author    = {Fedosov, Boris},
  title     = {Moduli spaces and deformation quantization in infinite dimensions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25396},
  year      = {1998},
  abstract  = {We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.},
  language  = {en}
}
@unpublished{Gilkey1998,
  author    = {Gilkey, Peter},
  title     = {The heat content asymptotics for variable geometries},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25381},
  year      = {1998},
  abstract  = {We study the heat content asymptotics on a compact manifold with boundary defened by a time dependent family of operators of Laplace type.},
  language  = {en}
}
@unpublished{Rebahi1998,
  author    = {Rebahi, Y.},
  title     = {Asymptotics of solutions of differential equations on manifolds with cusps},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25372},
  year      = {1998},
  language  = {en}
}
@unpublished{RabinovichSchulzeTarkhanov1998,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems in cuspidal wedges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25363},
  year      = {1998},
  abstract  = {The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges.},
  language  = {en}
}
@unpublished{Jaiani1998,
  author    = {Jaiani, George V.},
  title     = {Bending of an orthotropic cusped plate},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25356},
  year      = {1998},
  abstract  = {The bending of an orthotropic cusped plate in energetic and weighted Sobolev spaces has been considered. The existence and uniqueness of generalized and weak solutions of admissible boundary value problems (BVPs) have been investigated.},
  language  = {en}
}
@unpublished{Jaiani1998,
  author    = {Jaiani, George},
  title     = {On a mathematical model of a bar with variable rectangular cross-section},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25347},
  year      = {1998},
  abstract  = {Generalizing an idea of I. Vekua [1] who, in order to construct theory of plates and shells, fields of displacements, strains and stresses of threedimensional theory of linear elasticity expands into the orthogonal Fourier-series by Legendre Polynomials with respect to the variable along thickness, and then leaves only first N + 1, N = 0, 1, ..., terms, in the bar model under consideration all above quantities have been expanded into orthogonal double Fourier-series by Legendre Polynomials with respect to the variables along thickness, and width of the bar, and then first (Nsub(3) + 1)(Nsub(2) + 1), Nsub(3), Nsub(2) = 0, 1,..., terms have been left. This case will be called (Nsub(3), Nsub(2)) approximation. Both in general (Nsub(3), Nsub(2)) and in particular (0,0) (1,0) cases of approximation, the question of wellposedness of initial and boundary value problems, existence and uniqueness of solutions have been investigated. The cases when variable cross-section turns into segments of straight line, and points have been also considered. Such bars will be called cusped bars (see also [2]).},
  language  = {en}
}
@unpublished{ChenHidetoshi1998,
  author    = {Chen, Hua and Hidetoshi, Tahara},
  title     = {On the holomorphic solution of non-linear totally characteristic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25333},
  year      = {1998},
  abstract  = {The paper deals with a non-linear singular partial differential equation: (E) t∂/∂t = F(t, x, u, ∂u/∂x) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by G{\´e}rard-Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSternin1998,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25296},
  year      = {1998},
  abstract  = {For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space.},
  language  = {en}
}
@unpublished{SavinSchulzeSternin1998,
  author    = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {On the invariant index formulas for spectral boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25285},
  year      = {1998},
  abstract  = {In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSternin1998,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {The index of quantized contact transformations on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25276},
  year      = {1998},
  abstract  = {The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.},
  language  = {en}
}
@unpublished{Korkey1998,
  author    = {Korkey, Michael Brian},
  title     = {Optimal factorization of Muckenhoupt weights},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25266},
  year      = {1998},
  abstract  = {Peter Jones' theorem on the factorization of Ap weights is sharpened for weights with bounds near 1, allowing the factorization to be performed continuously near the limiting, unweighted case. When 1 < p < infinite and omega is an Ap weight with bound Ap(omega) = 1 + epsilon, it is shown that there exist Asub1 weights u, v such that both the formula omega = uv(1-p) and the estimates A1 (u), A1 (v) = 1 + Omikron (√epsilon) hold. The square root in these estimates is also proven to be the correct asymptotic power as epsilon -> 0.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Elliptic complexes of pseudodifferential operators on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25257},
  year      = {1998},
  abstract  = {On a compact closed manifold with edges live pseudodifferential operators which are block matrices of operators with additional edge conditions like boundary conditions in boundary value problems. They include Green, trace and potential operators along the edges, act in a kind of Sobolev spaces and form an algebra with a wealthy symbolic structure. We consider complexes of Fr{\´e}chet spaces whose differentials are given by operators in this algebra. Since the algebra in question is a microlocalization of the Lie algebra of typical vector fields on a manifold with edges, such complexes are of great geometric interest. In particular, the de Rham and Dolbeault complexes on manifolds with edges fit into this framework. To each complex there correspond two sequences of symbols, one of the two controls the interior ellipticity while the other sequence controls the ellipticity at the edges. The elliptic complexes prove to be Fredholm, i.e., have a finite-dimensional cohomology. Using specific tools in the algebra of pseudodifferential operators we develop a Hodge theory for elliptic complexes and outline a few applications thereof.},
  language  = {en}
}
@unpublished{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231},
  year      = {1998},
  abstract  = {Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.},
  language  = {en}
}
@unpublished{SchroheWalzeWarzecha1998,
  author    = {Schrohe, Elmar and Walze, Markus and Warzecha, Jan-Martin},
  title     = {Construction de Triplets Spectraux {\`a} Partir de Modules de Fredholm},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25247},
  year      = {1998},
  abstract  = {Soit (A, H, F) un module de Fredholm p-sommable, o{\`u} l'alg{\`e}bre A = CT est engendr{\´e}e par un groupe discret Gamma d'{\´e}l{\´e}ments unitaires de L(H) qui est de croissance polynomiale r. On construit alors un triplet spectral (A, H, D) sommabilit{\´e} q pour tout q > p + r + 1 avec F = signD. Dans le cas o{\`u} (A, H, F) est (p, infini)-sommable on obtient la (q, infini)-sommabilit{\´e} de (A, H, D)pour tout q > p + r + 1.},
  language  = {fr}
}
@unpublished{NacinovichSchulzeTarkhanov1998,
  author    = {Nacinovich, Mauro and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On carleman formulas for the dolbeault cohomology},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25224},
  year      = {1998},
  abstract  = {We discuss the Cauchy problem for the Dolbeault cohomology in a domain of C n with data on a part of the boundary. In this setting we introduce the concept of a Carleman function which proves useful in the study of uniqueness. Apart from an abstract framework we show explicit Carleman formulas for the Dolbeault cohomology.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Euler solutions of pseudodifferential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25211},
  year      = {1998},
  abstract  = {We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.},
  language  = {en}
}
@unpublished{LevendorskiiBoyarchenko1998,
  author    = {Levendorskii, Sergei Z. and Boyarchenko, Svetlana I.},
  title     = {Investment under uncertainty when shocks are non-gaussian},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25201},
  year      = {1998},
  language  = {en}
}
@unpublished{LevendorskiiBoyarchenko1998,
  author    = {Levendorskii, Sergei Z. and Boyarchenko, Svetlana I.},
  title     = {On rational pricing of derivative securities for a familiy of non-Gaussian processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25196},
  year      = {1998},
  abstract  = {Linear and non-linear analogues of the Black-Scholes equation are derived when shocks can be described by a truncated L{\´e}vy process. A linear equation is derived under the perfect correlation assumption on returns for a derivative security and a stock, and its solutions for European put and call options are obtained. It is also shown that the solution violates the perfect correlation assumption unless a process is gaussian. Thus, for a family of truncated L{\´e}vy distributions, the perfect hedging is impossible even in the continuous time limit. A second linear analogue of the Black-Scholes equation is obtained by constructing a portfolio which eliminates fluctuations of the first order and assuming that the portfolio is risk-free; it is shown that this assumption fails unless a process is gaussian. It is shown that the di erence between solutions to the linear analogues of the Black-Scholes equations and solutions to the Black-Scholes equations are sizable. The equations and solutions can be written in a discretized approximate form which uses an observed probability distribution only. Non-linear analogues for the Black-Scholes equation are derived from the non-arbitrage condition, and approximate formulas for solutions of these equations are suggested. Assuming that a linear generalization of the Black-Scholes equation holds, we derive an explicit pricing formula for the perpetual American put option and produce numerical results which show that the difference between our result and the classical Merton's formula obtained for gaussian processes can be substantial. Our formula uses an observed distribution density, under very weak assumptions on the latter.},
  language  = {en}
}
@unpublished{ChenLua1998,
  author    = {Chen, Hua and Lua, Zhuangehu},
  title     = {On the holomorphic solution of non-linear totally characteristic equations with several space variables},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25189},
  year      = {1998},
  abstract  = {In this paper we study a class of non-linear singular partial differential equation in complex domain Csub(t) x C n sub(x). Under certain assumptions, we prove the existence and uniqueness of holomorphic solution near origin of Csub(t) x C n sub(x).},
  language  = {en}
}
@unpublished{PaneahSchulze1998,
  author    = {Paneah, Boris and Schulze, Bert-Wolfgang},
  title     = {On the existence of smooth solutions of the dirichlet problem for hyperbolic : differential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25179},
  year      = {1998},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A remark on the index of symmetric operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169},
  year      = {1998},
  abstract  = {We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of higher order operators on singular surfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25127},
  year      = {1998},
  abstract  = {The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Lefschetz fixed point formula in the relative elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25159},
  year      = {1998},
  abstract  = {A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSterninetal.1997,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris and Shatalov, Victor},
  title     = {Spectral boundary value problems and elliptic equations on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25147},
  year      = {1997},
  abstract  = {For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On general boundary value problems for elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25138},
  year      = {1997},
  abstract  = {We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1997,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On the index formula for singular surfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25116},
  year      = {1997},
  abstract  = {In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.},
  language  = {en}
}
@unpublished{Fedosov1997,
  author    = {Fedosov, Boris},
  title     = {Non-Abelian reduction in deformation quantization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25101},
  year      = {1997},
  abstract  = {We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1997,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of elliptic operators on manifolds with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25096},
  year      = {1997},
  abstract  = {For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Quantization of symplectic transformations on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25084},
  year      = {1997},
  abstract  = {The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {A Lefschetz fixed point theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25073},
  year      = {1997},
  abstract  = {We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Operator algebras on singular manifolds. IV, V},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25062},
  year      = {1997},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The Riemann-Roch theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25051},
  year      = {1997},
  abstract  = {The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points.},
  language  = {en}
}
@unpublished{HieberSchrohe1997,
  author    = {Hieber, Matthias and Schrohe, Elmar},
  title     = {Lρ spectral independence of elliptic operators via commutator estimates},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25047},
  year      = {1997},
  abstract  = {Let {Tsub(p) : q1 ≤ p ≤ q2} be a family of consistent Csub(0) semigroups on Lφ(Ω) with q1, q2 ∈ [1, ∞)and Ω ⊆ IRn open. We show that certain commutator conditions on Tφ and on the resolvent of its generator Aφ ensure the φ independence of the spectrum of Aφ for φ ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with H{\"o}lder continuous coeffcients, Schr{\"o}dinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Operator algebras on singular manifolds. I},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25011},
  year      = {1997},
  language  = {en}
}
@unpublished{AirapetyanWitt1997,
  author    = {Airapetyan, Ruben and Witt, Ingo},
  title     = {Isometric properties of the Hankel Transformation in weighted sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25001},
  year      = {1997},
  abstract  = {It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.},
  language  = {en}
}
@unpublished{GalstianYagdjian1997,
  author    = {Galstian, Anahit and Yagdjian, Karen},
  title     = {Exponential function of pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24982},
  year      = {1997},
  abstract  = {The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Nonstationary problems for equations of Borel-Fuchs type},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24973},
  year      = {1997},
  abstract  = {In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On the index of differential operators on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24965},
  year      = {1997},
  abstract  = {The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.},
  language  = {en}
}