@unpublished{XiaochunSchulze2004,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@unpublished{SchulzeVolpato2004,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}
}
@book{SchulzeVolpato2004,
  author    = {Schulze, Bert-Wolfgang and Volpato, A.},
  title     = {Green operators in the edge calculus},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {24 S.},
  year      = {2004},
  language  = {en}
}
@article{SchulzeSeiler2004,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Boundary value problems with global projection conditions},
  issn      = {0022-1236},
  year      = {2004},
  abstract  = {Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved},
  language  = {en}
}
@article{RabinovichSchulzeTarkhanov2004,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems in oscillating cuspidal wedges},
  issn      = {0035-7596},
  year      = {2004},
  abstract  = {The paper is devoted to pseudodifferential boundary value problems in domains with 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}
}
@article{NazajkinskijSavinSterninetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Sternin, Boris Ju. and Schulze, Bert-Wolfgang},
  title     = {On the index of differential operators on manifolds with edges},
  issn      = {1064-5624},
  year      = {2004},
  language  = {en}
}
@article{NazajkinskijSavinSterninetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Sternin, Boris Ju. and Schulze, Bert-Wolfgang},
  title     = {On the existence of elliptic problems on manifolds with edges},
  issn      = {1064-5624},
  year      = {2004},
  language  = {en}
}
@article{NazajkinskijSavinSterninetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Sternin, Boris Ju. and Schulze, Bert-Wolfgang},
  title     = {Pseudodifferential operators on manifolds with edges},
  issn      = {1064-5624},
  year      = {2004},
  language  = {en}
}
@book{NazajkinskijSavinSchulzeetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {The index problem on manifolds with singularities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {27 S.},
  year      = {2004},
  language  = {en}
}
@book{NazajkinskijSavinSchulzeetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with edges},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {48 S.},
  year      = {2004},
  language  = {en}
}
@book{NazajkinskijSavinSchulzeetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {On the homotopy classification of elliptic operators on manifolds with edges},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {26 S.},
  year      = {2004},
  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{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{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}
}
@book{LiuSchulze2004,
  author    = {Liu, Xiaochun and Schulze, Bert-Wolfgang},
  title     = {Boundary value problems in edge representation},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {43 S.},
  year      = {2004},
  language  = {en}
}
@book{LiuSchulze2004,
  author    = {Liu, Xiaochun and Schulze, Bert-Wolfgang},
  title     = {Ellipticity on Manifolds with edges and boundary},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {35 S.},
  year      = {2004},
  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}
}
@book{KrainerSchulze2004,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {The Conormal symbolic structure of corner boundary value problems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {47 S.},
  year      = {2004},
  language  = {en}
}
@book{KapanadzeSchulze2004,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Boundary-contact Problems for Domains with Conical Singularities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {37 S.},
  year      = {2004},
  language  = {en}
}
@book{JaianiSchulze2004,
  author    = {Jaiani, George V. and Schulze, Bert-Wolfgang},
  title     = {Some degenerate elliptic systems and applications to cousped plates},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {33 S.},
  year      = {2004},
  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{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}
}
@book{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Boundary problems with meromorphic symbols in cylindrical domains},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {19 S.},
  year      = {2004},
  language  = {en}
}
@book{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The zaremba problem with singular interfaces as a corner boundary value problem},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {48 S.},
  year      = {2004},
  language  = {en}
}
@article{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Reduction of orders in boundary value problems without transmission property},
  issn      = {0025-5645},
  year      = {2004},
  abstract  = {Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We employ specific smooth symbols of arbitrary real orders and with parameters, and we show that the associated operators induce isomorphisms between Sobolev spaces on a given manifold with boundary. Such operators for integer orders have the transmission property and belong to the calculus of Boutet de Monvel [1], cf. also [9]. In general, they fit to the algebra of boundary value problems without the transmission property in the sense of [17] and [24]. Order reducing elements of the present kind are useful for constructing parametrices of mixed elliptic problems. We show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We then investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary. We finally construct order reducing operators on a compact manifold with conical singularities and boundary},
  language  = {en}
}
@article{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Parametrices of mixed elliptic problems},
  issn      = {0025-584X},
  year      = {2004},
  abstract  = {Mixed elliptic problems for differential operators A in a domain Q with smooth boundary Y are studied in the form Au = f in Omega, T+/-u = g+/- on Y+/-, where Y+/- subset of Y are manifolds with a common boundary Z, such that Y- boolean OR Y+ = Y and Y- boolean AND Y+ = z, with boundary conditions T+/- on Y+/- (with smooth coefficients up to Z from the respective side) satisfying the Shapiro-Lopatinskij condition. We consider such problems in standard Sobolev spaces and characterise natural extra conditions on the interface Z with an analogue of Shapiro-Lopatinskij ellipticity for an associated transmission problem on the boundary; then the extended operator is Fredholm. The transmission operators on the boundary with respect to Z belong to a complete pseudo-differential calculus, a modification of the algebra of boundary value problems without the transmission property. We construct parametrices of elliptic elements in that calculus, and we obtain parametrices of the original mixed problems under additional conditions on the interface. We consider the Zaremba problem and other mixed problems for the Laplace operator, determine the number of extra conditions and calculate the index of associated Fredholm operators. (C) 2004 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
  language  = {en}
}
@article{FedosovSchulzeTarkhanov2004,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On the index theorem for symplectic orbifolds},
  issn      = {0373-0956},
  year      = {2004},
  abstract  = {We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula},
  language  = {en}
}
@book{EgorovKondratievSchulze2004,
  author    = {Egorov, Yu. 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},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {21 S.},
  year      = {2004},
  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{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}
}
@book{CalvoMartinSchulze2004,
  author    = {Calvo, D. and Martin, Calin-Iulian and Schulze, Bert-Wolfgang},
  title     = {Symbolic Structures on Corner Manifolds},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {18 S.},
  year      = {2004},
  language  = {en}
}