@unpublished{HovhannisyanSchulze2010,
  author    = {Hovhannisyan, A. H. and Schulze, Bert-Wolfgang},
  title     = {On a method for solution of the ordinary differential equations connected with Huygens' equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-45381},
  year      = {2010},
  language  = {en}
}
@unpublished{MaSchulze2009,
  author    = {Ma, L. and Schulze, Bert-Wolfgang},
  title     = {Operators on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-36608},
  year      = {2009},
  abstract  = {We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 - γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.},
  language  = {en}
}
@unpublished{Schulze2009,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Boundary value problems with the transmission property},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30377},
  year      = {2009},
  abstract  = {We give a survey on the calculus of (pseudo-differential) boundary value problems with the transmision property at the boundary, and ellipticity in the Shapiro-Lopatinskij sense. Apart from the original results of the work of Boutet de Monvel we present an approach based on the ideas of the edge calculus. In a final section we introduce symbols with the anti-transmission property.},
  language  = {en}
}
@unpublished{AbedSchulze2009,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Edge-degenerate families of ΨDO's on an infinite cylinder},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30365},
  year      = {2009},
  abstract  = {We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.},
  language  = {en}
}
@unpublished{Schulze2008,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The iterative structure of corner operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30353},
  year      = {2008},
  abstract  = {We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference "Elliptic and Hyperbolic Equations on Singular Spaces", October 27 - 31, 2008, at the MSRI, University of Berkeley.},
  language  = {en}
}
@unpublished{Schulze2008,
  author    = {Schulze, Bert-Wolfgang},
  title     = {On a paper of Krupchyk, Tarkhanov, and Tuomela},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30325},
  year      = {2008},
  language  = {en}
}
@unpublished{SchulzeWei2008,
  author    = {Schulze, Bert-Wolfgang and Wei, Y.},
  title     = {Edge-boundary problems with singular trace conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30317},
  year      = {2008},
  abstract  = {The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (σψ; σ∂), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary we have a third symbolic component, namely the edge symbol σ∧, referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions in integral form' there may exist singular trace conditions, investigated in [6] on closed' manifolds with edge. Here we concentrate on the phenomena in combination with boundary conditions and edge problem.},
  language  = {en}
}
@unpublished{AbedSchulze2008,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Operators with corner-degenerate symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30299},
  year      = {2008},
  abstract  = {We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near the conical exit to infinity.},
  language  = {en}
}
@unpublished{FladSchneiderSchulze2007,
  author    = {Flad, Heinz-J{\"u}rgen and Schneider, Reinhold and Schulze, Bert-Wolfgang},
  title     = {Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30268},
  year      = {2007},
  abstract  = {We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.},
  language  = {en}
}
@unpublished{Schulze2006,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential calculus on manifolds with geometric singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30204},
  year      = {2006},
  abstract  = {Differential and pseudo-differential operators on a manifold with (regular) geometric singularities can be studied within a calculus, inspired by the concept of classical pseudo-differential operators on a C1 manifold. In the singular case the operators form an algebra with a principal symbolic hierarchy σ = (σj)0≤j≤k, with k being the order of the singularity and σk operator-valued for k ≥ 1. The symbols determine ellipticity and the nature of parametrices. It is typical in this theory that, similarly as in boundary value problems (which are special edge problems, where the edge is just the boundary), there are trace, potential and Green operators, associated with the various strata of the configuration. The operators, obtained from the symbols by various quantisations, act in weighted distribution spaces with multiple weights. We outline some essential elements of this calculus, give examples and also comment on new challenges and interesting problems of the recent development.},
  language  = {en}
}
@unpublished{Schulze2006,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Elliptic differential operators on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30188},
  year      = {2006},
  abstract  = {On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.},
  language  = {en}
}
@unpublished{HarutyunyanSchulze2006,
  author    = {Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Boundary value problems in weighted edge spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30104},
  year      = {2006},
  abstract  = {We study elliptic boundary value problems in a wedge with additional edge conditions of trace and potential type. We compute the (difference of the) number of such conditions in terms of the Fredholm index of the principal edge symbol. The task will be reduced to the case of special opening angles, together with a homotopy argument.},
  language  = {en}
}
@unpublished{Schulze2006,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The structure of operators on manifolds with polyhedral singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30099},
  year      = {2006},
  abstract  = {We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.},
  language  = {en}
}
@unpublished{KapanadzeSchulzeSeiler2006,
  author    = {Kapanadze, D. and Schulze, Bert-Wolfgang and Seiler, J.},
  title     = {Operators with singular trace conditions on a manifold with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30058},
  year      = {2006},
  abstract  = {We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions of that kind in integral form we admit in this paper 'singular' trace, potential and Green operators, which are related to the corresponding operators of positive type in Boutet de Monvel's calculus for boundary value problems.},
  language  = {en}
}
@unpublished{MartinSchulze2005,
  author    = {Martin, C.-I. and Schulze, Bert-Wolfgang},
  title     = {The quantisation of edge symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29959},
  year      = {2005},
  abstract  = {We investigate operators on manifolds with edges from the point of view of the symbolic calculus induced by the singularities. We discuss new aspects of the quantisation of edge-degenerate symbols which lead to continuous operators in weighted edge spaces.},
  language  = {en}
}
@unpublished{KapanadzeSchulze2005,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Boundary-contact problems for domains with edge singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29901},
  year      = {2005},
  abstract  = {We study boundary-contact problems for elliptic equations (and systems) with interfaces that have edge singularities. Such problems represent continuous operators between weighted edge spaces and subspaces with asymptotics. Ellipticity is formulated in terms of a principal symbolic hierarchy, containing interior, transmission, and edge symbols. We construct parametrices, show regularity with asymptotics of solutions in weighted edge spaces and illustrate the results by boundary-contact problems for the Laplacian with jumping coefficients.},
  language  = {en}
}
@unpublished{SchulzeQin2005,
  author    = {Schulze, Bert-Wolfgang and Qin, Yuming},
  title     = {Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29892},
  year      = {2005},
  abstract  = {In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2005,
  author    = {Harutjunjan, G. and Schulze, Bert-Wolfgang},
  title     = {Conormal symbols of mixed elliptic problems with singular interfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29885},
  year      = {2005},
  abstract  = {Mixed elliptic problems are characterised by conditions that have a discontinuity on an interface of the boundary of codimension 1. The case of a smooth interface is treated in [3]; the investigation there refers to additional interface conditions and parametrices in standard Sobolev spaces. The present paper studies a necessary structure for the case of interfaces with conical singularities, namely, corner conormal symbols of such operators. These may be interpreted as families of mixed elliptic problems on a manifold with smooth interface. We mainly focus on second order operators and additional interface conditions that are holomorphic in an extra parameter. In particular, for the case of the Zaremba problem we explicitly obtain the number of potential conditions in this context. The inverses of conormal symbols are meromorphic families of pseudo-differential mixed problems referring to a smooth interface. Pointwise they can be computed along the lines [3].},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2005,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems with Toeplitz conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29837},
  year      = {2005},
  abstract  = {We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which serve as domains of pseudodifferential operators and which fit well to the nature of operators.},
  language  = {en}
}
@unpublished{CalvoSchulze2005,
  author    = {Calvo, D. and Schulze, Bert-Wolfgang},
  title     = {Operators on corner manifolds with exit to infinity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29753},
  year      = {2005},
  abstract  = {We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo 'lower order terms') by a principal symbolic hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and σ ^(A)(y, η), (y, η) 2 T*Y \ 0, the (operator-valued) edge symbol of 'first generation', cf. [15]. The novelty here is the edge symbol σ^ of 'second generation', parametrised by (z, Ϛ) 2 T*Z \ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.},
  language  = {en}
}
@unpublished{JaianiSchulze2004,
  author    = {Jaiani, George and Schulze, Bert-Wolfgang},
  title     = {Some degenerate elliptic systems and applications to cusped plates},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26866},
  year      = {2004},
  abstract  = {The tension-compression vibration of an elastic cusped plate is studied under all the reasonable boundary conditions at the cusped edge, while at the noncusped edge displacements and at the upper and lower faces of the plate stresses are given.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem with singular interfaces as a corner boundary value problem},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26855},
  year      = {2004},
  abstract  = {We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y , i.e., Au = f in int X, T±u = g± on int Y±, where Y is subdivided into subsets Y± with an interface Z and boundary conditions T± on Y± that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z ⊂ Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in [3]. With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z \ {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.},
  language  = {en}
}
@unpublished{SchulzeVolpato2004,
  author    = {Schulze, Bert-Wolfgang and Volpato, A.},
  title     = {Green operators in the edge calculus},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26846},
  year      = {2004},
  abstract  = {Green operators on manifolds with edges are known to be an ingredient of parametrices of elliptic (edge-degenerate) operators. They play a similar role as corresponding operators in boundary value problems. Close to edge singularities the Green operators have a very complex asymptotic behaviour. We give a new characterisation of Green edge symbols in terms of kernels with discrete and continuous asymptotics in the axial variable of local model cones.},
  language  = {en}
}
@unpublished{DinesLiuSchulze2004,
  author    = {Dines, Nicoleta and Liu, X. and Schulze, Bert-Wolfgang},
  title     = {Edge quantisation of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26838},
  year      = {2004},
  abstract  = {The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.},
  language  = {en}
}
@unpublished{EgorovKondratievSchulze2004,
  author    = {Egorov, Jurij V. and Kondratiev, V. A. and Schulze, Bert-Wolfgang},
  title     = {On the completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26773},
  year      = {2004},
  abstract  = {Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Proof of Theorem 2. 5 The growth of the resolvent 6 Proof of Theorem 3. 7 The completeness of root functions 8 Some generalizations},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2004,
  author    = {Nazaikinskii, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {On the homotopy classification of elliptic operators on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26769},
  year      = {2004},
  abstract  = {We obtain a stable homotopy classification of elliptic operators on manifolds with edges.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2004,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 6: Elliptic theory on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26757},
  year      = {2004},
  abstract  = {Contents: Chapter 6: Elliptic Theory on Manifolds with Edges Introduction 6.1. Motivation and Main Constructions 6.1.1. Manifolds with edges 6.1.2. Edge-degenerate differential operators 6.1.3. Symbols 6.1.4. Elliptic problems 6.2. Pseudodifferential Operators 6.2.1. Edge symbols 6.2.2. Pseudodifferential operators 6.2.3. Quantization 6.3. Elliptic Morphisms and the Finiteness Theorem 6.3.1. Matrix Green operators 6.3.2. General morphisms 6.3.3. Ellipticity, Fredholm property, and smoothness Appendix A. Fiber Bundles and Direct Integrals A.1. Local theory A.2. Globalization A.3. Versions of the Definition of the Norm},
  language  = {en}
}
@unpublished{XiaochunSchulze2004,
  author    = {Xiaochun, Liu and Schulze, Bert-Wolfgang},
  title     = {Boundary value problems in edge representation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26746},
  year      = {2004},
  abstract  = {Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Boundary problems with meromorphic symbols in cylindrical domains},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26735},
  year      = {2004},
  abstract  = {We show relative index formulas for boundary value problems in cylindrical domains and Sobolev spaces with different weigths at ±∞. The amplitude functions are meromorphic in the axial covariable and take values in the space of boundary value problems on the cross section of the cylinder.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2004,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26700},
  year      = {2004},
  abstract  = {Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks},
  language  = {en}
}
@unpublished{KrainerSchulze2004,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {The conormal symbolic structure of corner boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26662},
  year      = {2004},
  abstract  = {Ellipticity of operators on manifolds with conical singularities or parabolicity on space-time cylinders are known to be linked to parameter-dependent operators (conormal symbols) on a corresponding base manifold. We introduce the conormal symbolic structure for the case of corner manifolds, where the base itself is a manifold with edges and boundary. The specific nature of parameter-dependence requires a systematic approach in terms of meromorphic functions with values in edge-boundary value problems. We develop here a corresponding calculus, and we construct inverses of elliptic elements.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2003,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 5: Manifolds with isolated singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26659},
  year      = {2003},
  abstract  = {Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Ellipticity and the finiteness theorem 5.4. Calculus of ΨDO 5.4.1. General ΨDO 5.4.2. The subalgebra of stabilizing ΨDO 5.4.3. Ellipticity and the finiteness theorem},
  language  = {en}
}
@unpublished{DinesSchulze2003,
  author    = {Dines, Nicoleta and Schulze, Bert-Wolfgang},
  title     = {Mellin-edge representations of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26627},
  year      = {2003},
  abstract  = {We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.},
  language  = {en}
}
@unpublished{DinesHarutjunjanSchulze2003,
  author    = {Dines, Nicoleta and Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem in edge Sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26615},
  year      = {2003},
  abstract  = {Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.},
  language  = {en}
}
@unpublished{Schulze2003,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Crack theory with singularties at the boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26600},
  year      = {2003},
  abstract  = {We investigate crack problems, where the crack boundary has conical singularities. Elliptic operators with two-sided elliptc boundary conditions on the plus and minus sides of the crack will be interpreted as elements of a corner algebra of boundary value problems. The corresponding operators will be completed by extra edge conditions on the crack boundary to Fredholm operators in corner Sobolev spaces with double weights, and there are parametrices within the calculus.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2003,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 3: Eta invariant and the spectral flow},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26595},
  year      = {2003},
  abstract  = {Contents: Chapter 3: Eta Invariant and the Spectral Flow 3.1. Introduction 3.2. The Classical Spectral Flow 3.2.1. Definition and main properties 3.2.2. The spectral flow formula for periodic families 3.3. The Atiyah-Patodi-Singer Eta Invariant 3.3.1. Definition of the eta invariant 3.3.2. Variation under deformations of the operator 3.3.3. Homotopy invariance. Examples 3.4. The Eta Invariant of Families with Parameter (Melrose's Theory) 3.4.1. A trace on the algebra of parameter-dependent operators 3.4.2. Definition of the Melrose eta invariant 3.4.3. Relationship with the Atiyah-Patodi-Singer eta invariant 3.4.4. Locality of the derivative of the eta invariant. Examples 3.5. The Spectral Flow of Families of Parameter-Dependent Operators 3.5.1. Meromorphic operator functions. Multiplicities of singular points 3.5.2. Definition of the spectral flow 3.6. Higher Spectral Flows 3.6.1. Spectral sections 3.6.2. Spectral flow of homotopies of families of self-adjoint operators 3.6.3. Spectral flow of homotopies of families of parameter-dependent operators 3.7. Bibliographical Remarks},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2003,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 4: Pseudodifferential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26587},
  year      = {2003},
  abstract  = {Contents: Chapter 4: Pseudodifferential Operators 4.1. Preliminary Remarks 4.1.1. Why are pseudodifferential operators needed? 4.1.2. What is a pseudodifferential operator? 4.1.3. What properties should the pseudodifferential calculus possess? 4.2. Classical Pseudodifferential Operators on Smooth Manifolds 4.2.1. Definition of pseudodifferential operators on a manifold 4.2.2. H{\"o}rmander's definition of pseudodifferential operators 4.2.3. Basic properties of pseudodifferential operators 4.3. Pseudodifferential Operators in Sections of Hilbert Bundles 4.3.1. Hilbert bundles 4.3.2. Operator-valued symbols. Specific features of the infinite-dimensional case 4.3.3. Symbols of compact fiber variation 4.3.4. Definition of pseudodifferential operators 4.3.5. The composition theorem 4.3.6. Ellipticity 4.3.7. The finiteness theorem 4.4. The Index Theorem 4.4.1. The Atiyah-Singer index theorem 4.4.2. The index theorem for pseudodifferential operators in sections of Hilbert bundles 4.4.3. Proof of the index theorem 4.5. Bibliographical Remarks},
  language  = {en}
}
@unpublished{DeDonnoSchulze2003,
  author    = {De Donno, G. and Schulze, Bert-Wolfgang},
  title     = {Meromorphic symbolic structures for boundary value problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26570},
  year      = {2003},
  abstract  = {We investigate the ideal of Green and Mellin operators with asymtotics for a manifold with edge-corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov2003,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On index theorem for symplectic orbifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26550},
  year      = {2003},
  abstract  = {We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2003,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 1: Localization (surgery) in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26546},
  year      = {2003},
  abstract  = {Contents: Chapter 1: Localization (Surgery) in Elliptic Theory 1.1. The Index Locality Principle 1.1.1. What is locality? 1.1.2. A pilot example 1.1.3. Collar spaces 1.1.4. Elliptic operators 1.1.5. Surgery and the relative index theorem 1.2. Surgery in Index Theory on Smooth Manifolds 1.2.1. The Booß-Wojciechowski theorem 1.2.2. The Gromov-Lawson theorem 1.3. Surgery for Boundary Value Problems 1.3.1. Notation 1.3.2. General boundary value problems 1.3.3. A model boundary value problem on a cylinder 1.3.4. The Agranovich-Dynin theorem 1.3.5. The Agranovich theorem 1.3.6. Bojarski's theorem and its generalizations 1.4. (Micro)localization in Lefschetz theory 1.4.1. The Lefschetz number 1.4.2. Localization and the contributions of singular points 1.4.3. The semiclassical method and microlocalization 1.4.4. The classical Atiyah-Bott-Lefschetz theorem},
  language  = {en}
}
@unpublished{KapanadzeSchulze2003,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Asymptotics of potentials in the edge calculus},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26530},
  year      = {2003},
  abstract  = {Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by sbmanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous perators between cone or edge Sobolev spaces and subspaces with asymptotics.},
  language  = {en}
}
@unpublished{Schulze2003,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Toeplitz operators, and ellipticity of boundary value problems with global projection conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26510},
  year      = {2003},
  abstract  = {Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2003,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : V. Index formulas for elliptic problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26500},
  year      = {2003},
  abstract  = {For elliptic problems on manifolds with edges, we construct index formulas in form of a sum of homotopy invariant contributions of the strata (the interior of the manifold and the edge). Both terms are the indices of elliptic operators, one of which acts in spaces of sections of finite-dimensional vector bundles on a compact closed manifold and the other in spaces of sections of infinite-dimensional vector bundles over the edge.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2002,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Asymptotics and relative index on a cylinder with conical cross section},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26446},
  year      = {2002},
  abstract  = {We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula.},
  language  = {en}
}
@unpublished{CoriascoSchulze2002,
  author    = {Coriasco, Sandro and Schulze, Bert-Wolfgang},
  title     = {Edge problems on configurations with model cones of different dimensions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26438},
  year      = {2002},
  abstract  = {Elliptic equations on configurations W = W1 ∪ ... ∪ Wn with edge Y and components Wj of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here, edges. Starting from edge-degenerate operators on Wj, j = 1, ..., N, we construct an algebra with extra "transmission" conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator-valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on W\Y. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics.},
  language  = {en}
}
@unpublished{OliaroSchulze2002,
  author    = {Oliaro, Alessandro and Schulze, Bert-Wolfgang},
  title     = {Parameter-dependent boundary value problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26424},
  year      = {2002},
  abstract  = {As is known from Kondratyev's work, boundary value problems for elliptic operators on a manifold with conical singularities and boundary are controlled by a principal symbolic hierarchy, where the conormal symbols belong to the typical new components, compared with the smooth case, with interior and boundary symbols. A similar picture may be expected on manifolds with corners when the base of the cone itself is a manifold with conical or edge singularities. This is a natural situation in a number of applications, though with essential new difficulties. We investigate here corresponding conormal symbols in terms of a calculus of holomorphic parameter-dependent edge boundary value problems on the base. We show that a certain kernel cut-off procedure generates all such holomorphic families, modulo smoothing elements, and we establish conormal symbols as an algebra as is necessary for a parametrix constructions in the elliptic case.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26415},
  year      = {2002},
  abstract  = {The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26386},
  year      = {2002},
  abstract  = {When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.},
  language  = {en}
}
@unpublished{ManicciaSchulze2002,
  author    = {Maniccia, L. and Schulze, Bert-Wolfgang},
  title     = {An algebra of meromorphic corner symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26360},
  year      = {2002},
  abstract  = {Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26335},
  year      = {2002},
  abstract  = {Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.},
  language  = {en}
}