@unpublished{Krainer2001,
  author    = {Krainer, Thomas},
  title     = {The calculus of Volterra Mellin pseudodifferential operators with operator-valued symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26185},
  year      = {2001},
  abstract  = {We introduce the calculus of Mellin pseudodifferential operators parameters based on "twisted" operator-valued Volterra symbols as well aas the abstract Mellin calclus with holomorphic symbols. We establish the properties of the symblic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side, e. g., for the Leibniz-product, kernel cut-off, and Mellin quantization. Moreover, we introduce the notion of parabolicity for the calculi of Volterra Mellin operators, and construct Volterra parametrices for parabolic operators within the calculi.},
  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@unpublished{CoriascoSchroheSeiler2001,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@unpublished{XiaochunWitt2001,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{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{JunkerSchrohe2001,
  author    = {Junker, Wolfgang and Schrohe, Elmar},
  title     = {Adiabatic vacuum states on general spacetime manifolds : definition, construction, and physical properties},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26100},
  year      = {2001},
  abstract  = {Adiabatic vacuum states are a well-known class of physical states for linear quantum fields n Robertson-Walker spacetimes. We extend the definition of adiabatic vacua to general spacetime manifolds by using the notion of the Sobolev wavefront set. This definition is also applicable to interacting field theories. Hadamard states form a special subclass of the adiabatic vacua. We analyze physical properties of adiabatic vacuum representations of the Klein-Gordon field on globally hyperbolic spacetme manifolds (factoriality, quasiequivalence, local definteness, Haag duality) and construct them explicitly, if the manifold has a compact Cauchy surface.},
  language  = {en}
}
@unpublished{Yagdjian2001,
  author    = {Yagdjian, Karen},
  title     = {Geometric optics for the nonlinear hyperbolic systems of Kirchhoff-type},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26059},
  year      = {2001},
  abstract  = {Contents: 1 Introduction 2 Main result 3 Construction of the asymptotic solutions 3.1 Derivation of the equations for the profiles 3.2 Exsistence of the principal profile 3.3 Determination of Usub(2) and the remaining profiles 4 Stability of the samll global solutions. Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations 4.1 Stability of the global solutions to the Kirchhoff-type symmetric hyperbolic systems 4.2 The nonlinear system of ordinary differential equations with the parameter 4.3 Some energies estimates 4.4 The dependence of the solution W(t, ξ) on the function s(t) 4.5 The oscillatory integrals of the bilinear forms of the solutions 4.6 Estimates for the basic bilinear form Γsub(s)(t) 4.7 Contraction mapping 4.8 Stability of the global solution 4.9 Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations},
  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{Galstian2001,
  author    = {Galstian, Anahit},
  title     = {Lp - Lq decay estimates for the equation with exponentially growing coefficient},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26079},
  year      = {2001},
  abstract  = {Contents: 1 Introduction 1 Representation formulas 2 Consideration in the pseudodifferential zone: e up(t) |ξ| ≤ 1 3 Consideration in he hyperbolic zone: e up(t) |ξ| ≥ 1},
  language  = {en}
}
@unpublished{Harutyunyan2001,
  author    = {Harutyunyan, Anahit V.},
  title     = {Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26110},
  year      = {2001},
  abstract  = {This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved.},
  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{NazaikinskiiSternin2001,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {Some problems of control of semiclassical states for the Schr{\"o}dinger equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26130},
  year      = {2001},
  abstract  = {Contents: Introduction Controlled Quantum Systems The Asymptotic Controllability Problem The Stabilization Problem Unitarily Nonlinear Equations The Quantum Problem The Stabilization Problem for the Schr{\"o}dinger Equation with a Unitarily Non-linear Control},
  language  = {en}
}
@unpublished{Witt2001,
  author    = {Witt, Ingo},
  title     = {Asymptotic algebras},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26069},
  year      = {2001},
  abstract  = {The concept of asymptotic type that primarily appears in singular and asymptotic analysis is developed. Especially, asymptotic algebras are introduced.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2001,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Duality by reproducing kernels},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26095},
  year      = {2001},
  abstract  = {Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A.},
  language  = {en}
}
@unpublished{PrenovTarkhanov2001,
  author    = {Prenov, B. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Kernel spikes of singular problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26195},
  year      = {2001},
  abstract  = {Function spaces with asymptotics is a usual tool in the analysis on manifolds with singularities. The asymptotics are singular ingredients of the kernels of pseudodifferential operators in the calculus. They correspond to potentials supported by the singularities of the manifold, and in this form asymptotics can be treated already on smooth configurations. This paper is aimed at describing refined asymptotics in the Dirichlet problem in a ball. The beauty of explicit formulas highlights the structure of asymptotic expansions in the calculi on singular varieties.},
  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{Paneah2001,
  author    = {Paneah, Boris},
  title     = {On a new problem in integral geometry related to boundary problems for partial differential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26089},
  year      = {2001},
  abstract  = {Contents: 1 Introduction 2 Statement of the problem and definitions 3 The main results 4 Proof of theorem 2 4.1 Reduction of problem (2) to functional - integral equations 4.2 The uniqueness of a solution of equation (2) 4.3 The existence of a solution of equation (2) 5 Proof of theorem 1 6 Proof of theorem 3 7 First boundary problem for hyperbolic differential equations 7.1 Statement of the problem 7.2 The formulation of the result and a sketch of the proof},
  language  = {en}
}
@unpublished{Messina2001,
  author    = {Messina, Francesca},
  title     = {Local solvability for semilinear Fuchsian equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26124},
  year      = {2001},
  abstract  = {Contents: 1 Introduction 2 Differential operators on manifolds with conical singularities 3 When H up(s,y) (B) is an algebra 4 Statement of the main result 5 Proof of the theorem},
  language  = {en}
}
@unpublished{SavinSternin2001,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Index defects in the theory of nonlocal boundary value problems and the η-invariant},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26146},
  year      = {2001},
  abstract  = {The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincar{\´e} duality in the K-theory of the corresponding manifolds with singularities.},
  language  = {en}
}
@unpublished{ChenYu2001,
  author    = {Chen, Hua and Yu, Chun},
  title     = {Asymptotic behaviour of the trace for Schr{\"o}dinger operator on fractal drums},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26157},
  year      = {2001},
  language  = {en}
}
@unpublished{MeloNestSchrohe2001,
  author    = {Melo, S. T. and Nest, R. and Schrohe, Elmar},
  title     = {C*-structure and K-theory of Boutet de Monvel's algebra},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26166},
  year      = {2001},
  abstract  = {We consider the norm closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a manifold X with boundary ∂X. We first describe the image and the kernel of the continuous extension of the boundary principal symbol homomorphism to A. If X is connected and ∂X is not empty, we then show that the K-groups of A are topologically determined. In case the manifold, its boundary, and the cotangent space of its interior have torsion free K-theory, we get Ki(A,k) congruent Ki(C(X))⊕Ksub(1-i)(Csub(0)(T*X)),i = 0,1, with k denoting the compact ideal, and T*X denoting the cotangent bundle of the interior. Using Boutet de Monvel's index theorem, we also prove that the above formula holds for i = 1 even without this torsion-free hypothesis. For the case of orientable, two-dimensional X, Ksub(0)(A) congruent Z up(2g+m) and Ksub(1)(A) congruent Z up(2g+m-1), where g is the genus of X and m is the number of connected components of ∂X. We also obtain a composition sequence 0 ⊂ k ⊂ G ⊂ A, with A/G commutative and G/k isomorphic to the algebra of all continuous functions on the cosphere bundle of ∂X with values in compact operators on L²(R+).},
  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{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{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 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{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{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{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{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{NazaikinskiiSchulzeSternin2001,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Localization problem in index theory of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26175},
  year      = {2001},
  abstract  = {This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.},
  language  = {en}
}