TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Lyu, Xiaojing
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent edge calculus and corner parametrices
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case.
KW  - Edge calculus
KW  - corner parametrices
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 12
SP  - 2021
EP  - 2051
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - BOOK
A1  - Oliaro, A.
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent Boundary value problems on manifolds with edges
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Oliaro, Alessandro
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent boundary value problems on manifolds with edges
N2  - 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.
T3  - Preprint - (2002) 25 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26424
ER  - 
TY  - BOOK
A1  - Albeverio, Sergio
A1  - Demuth, Michael
A1  - Schrohe, Elmar
A1  - Schulze, Bert-Wolfgang
T1  - Parabolicity, volterra calculus, and conical singularities : a volume of advances in partial differential equations
T3  - Operator theory : advances and applications
Y1  - 2002
SN  - 3-7643-6906-x
VL  - 138
PB  - Birkhäuser Verl.
CY  - Basel
ER  - 
TY  - JOUR
A1  - Lyu, Xiaojing
A1  - Qian, Tao
A1  - Schulze, Bert-Wolfgang
T1  - Order filtrations of the edge algebra
JF  - Journal of pseudo-differential operators and applications
N2  - By edge algebra we understand a pseudo-differential calculus on a manifold with edge. The operators have a two-component principal symbolic hierarchy which determines operators up to lower order terms. Those belong to a filtration of the corresponding operator spaces. We give a new characterisation of this structure, based on an alternative representation of edge amplitude functions only containing holomorphic edge-degenerate Mellin symbols.
Y1  - 2015
U6  - https://doi.org/10.1007/s11868-015-0126-8
SN  - 1662-9981
SN  - 1662-999X
VL  - 6
IS  - 3
SP  - 279
EP  - 305
PB  - Springer
CY  - Basel
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Operators with symbol hierarchies and iterated asymptotics
N2  - 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
T3  - Preprint - (2001) 10 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25948
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - Operators with symbol hierarchies and iterated asymptotics
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Operators with singular trace conditions on a manifold with edges
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Kapanadze, D.
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, J.
T1  - Operators with singular trace conditions on a manifold with edges
N2  - 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.
T3  - Preprint - (2006) 01 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30058
ER  - 
TY  - BOOK
A1  - Abed, Jamil
A1  - Schulze, Bert-Wolfgang
T1  - Operators with Corner-degenerate Symbols
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2008
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Abed, Jamil
A1  - Schulze, Bert-Wolfgang
T1  - Operators with corner-degenerate symbols
N2  - 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.
T3  - Preprint - (2008) 01 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30299
ER  - 
TY  - INPR
A1  - Ma, L.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on manifolds with conical singularities
N2  - 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.
T3  - Preprint - (2009) 07 
KW  - Operators on manifolds with conical singularities
KW  - conormal symbols
KW  - ellipticity of cone operators
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-36608
ER  - 
TY  - BOOK
A1  - Calvo, D.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on Corner Manifolds with Exit to Infinity
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Calvo, D.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on corner manifolds with exit to infinity
N2  - 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.
T3  - Preprint - (2005) 01 
KW  - Operators on manifolds with edge and conical exit to infinity
KW  - Sobolev spaces with double weights on singular cones
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29753
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - Operator algebras with symbol hierarchies on manifolds with singularities
Y1  - 2001
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - Operator algebras with symbol hierarchies on manifolds with singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Operator algebras with symbol hierarchies on manifolds with singularities
N2  - Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.
T3  - Preprint - (1999) 30 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25647
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - Operator algebras on singular manifolds. IV, V
T3  - Preprint - (1997) 19 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25062
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - Operator algebras on singular manifolds. I
T3  - Preprint - (1997) 16 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25011
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Operator algebras associated with resurgent transforms and differential equations on manifolds with singularities
Y1  - 1997
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 3: Chapter 6+7]
N2  - 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.
T3  - Preprint - (2001) 16 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26000
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 2: Chapter 3-5]
N2  - 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.
T3  - Preprint - (2001) 15 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25992
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 1: Chapter 1+2]
N2  - 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.
T3  - Preprint - (2001) 14 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25987
ER  - 
TY  - BOOK
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equation of german form in an infinite space-time cylinder : Charpters III - V
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equation of general form in an infinite space-time cylinder : Chapters VI - VII
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equation of general form in an infinite space-time cylinder : Chapters I - II
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - On the invariant index formulas for spectral boundary value problems
N2  - In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms.
T3  - Preprint - (1998) 18 
KW  - spectral boundary value problems
KW  - Fredholm property
KW  - index of elliptic operator
KW  - Chern character
KW  - Atiyah-Patodi-Singer theory
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25285
ER  - 
TY  - JOUR
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - On the invariant index formulas for spectral boundary value problems
Y1  - 1999
ER  - 
TY  - BOOK
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - On the invariant index formulas for spectral boundary value problems
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1998
VL  - 1998, 18b
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On the index theorem for symplectic orbifolds
N2  - We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula
Y1  - 2004
SN  - 0373-0956
ER  - 
TY  - JOUR
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - On the index of elliptice operators on a wedge
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
A1  - Schulze, Bert-Wolfgang
T1  - On the index of elliptic operators on manifolds with edges
N2  - Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables
Y1  - 2005
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On the index of elliptic operators on manifolds with conical singularities
Y1  - 1999
SN  - 0002-3264
SN  - 0869-5652
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
A1  - Schulze, Bert-Wolfgang
T1  - On the index of differential operators on manifolds with edges
Y1  - 2004
SN  - 1064-5624
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - On the index of differential operators on manifolds with conical singularities
N2  - The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.
T3  - Preprint - (1997) 10 
KW  - conical singularities
KW  - Mellin transform
KW  - pseudodiferential operators
KW  - ellipticity
KW  - Fredholm operators
KW  - regularizers
KW  - analytic index
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24965
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On the index of differential operators on manifolds with conical singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 10
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On the index of differential operators on manifolds with conical singularities
Y1  - 1998
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On the index formula for singular surfaces
N2  - In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.
T3  - Preprint - (1997) 31 
KW  - manifolds with singularities
KW  - differential operators
KW  - index
KW  - 'eta' invariant
KW  - monodromy matrix
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25116
ER  - 
TY  - BOOK
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - On the index formula for singular surfaces
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 31
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - On the index formula for singular surfaces
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
T1  - On the index elliptic operators on a cone
Y1  - 1996
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Nazaikinskii, Vladimir E.
A1  - Sternin, Boris
T1  - On the homotopy classification of elliptic operators on manifolds with singularities
N2  - We study the homotopy classification of elliptic operators on manifolds with singularities and establish necessary and sufficient conditions under which the classification splits into terms corresponding to the principal symbol and the conormal symbol.
T3  - Preprint - (1999) 21 
KW  - elliptic operators
KW  - homotopy classification
KW  - manifold with singularities
KW  - Atiyah-Singer theorem
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25574
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Nazajkinskij, Vladimir E.
A1  - Sternin, Boris Ju.
T1  - On the homotopy classification of elliptic operators on manifolds with singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir E.
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - On the homotopy classification of elliptic operators on manifolds with edges
N2  - We obtain a stable homotopy classification of elliptic operators on manifolds with edges.
T3  - Preprint - (2004) 16 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26769
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - On the homotopy classification of elliptic operators on manifolds with edges
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Paneah, Boris
A1  - Schulze, Bert-Wolfgang
T1  - On the existence of smooth solutions of the Dirichlet problem for hyperbolic differential equations
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1998
VL  - 1998, 05
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Paneah, Boris
A1  - Schulze, Bert-Wolfgang
T1  - On the existence of smooth solutions of the dirichlet problem for hyperbolic : differential equations
T3  - Preprint - (1998) 05 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25179
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
A1  - Schulze, Bert-Wolfgang
T1  - On the existence of elliptic problems on manifolds with edges
Y1  - 2004
SN  - 1064-5624
ER  - 
TY  - INPR
A1  - Egorov, Jurij V.
A1  - Kondratiev, V. A.
A1  - Schulze, Bert-Wolfgang
T1  - On the completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary
N2  - 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
T3  - Preprint - (2004) 17 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26773
ER  - 
TY  - BOOK
A1  - Egorov, Yu.
A1  - Kondratiev, V. A.
A1  - Schulze, Bert-Wolfgang
T1  - On the completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On some global aspects of the theory of partial differential equations on manifolds with singularities
Y1  - 1998
ER  - 
TY  - BOOK
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On index theorem for symplectic orbifolds
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On index theorem for symplectic orbifolds
N2  - We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula.
T3  - Preprint - (2003) 07 
KW  - star product
KW  - symmetry group
KW  - G-trace
KW  - G-index
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26550
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - On general boundary value problems for elliptic equations
N2  - We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.
T3  - Preprint - (1997) 35 
KW  - elliptic boundary value problems
KW  - Atiyah-Bott condition
KW  - Calderón projections
KW  - Cauchy Riemann operator
KW  - Euler operator
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25138
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On general boundary value problems for elliptic equations
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 35
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On general boundary value problems for elliptic equations
Y1  - 1998
SN  - 0368-8666
SN  - 0025-5157
SN  - 0321-4540
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On general boundary value problems for elliptic equations
Y1  - 1998
ER  - 
TY  - INPR
A1  - Egorov, Yu.
A1  - Kondratiev, V.
A1  - Schulze, Bert-Wolfgang
T1  - On completeness of eigenfunctions of an elliptic operator on a manifold with conical points
N2  - Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Completeness of root functions
T3  - Preprint - (2001) 04 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25937
ER  - 
TY  - BOOK
A1  - Egorov, Yu
A1  - Kondratiev, V. A.
A1  - Schulze, Bert-Wolfgang
T1  - On completeness of eigenfunctions of an elliptic operator on a manifold with concial points
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgrupe Partielle Differentialgleichun
Y1  - 2001
SN  - 1437-339X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Nacinovich, Mauro
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On carleman formulas for the dolbeault cohomology
N2  - We discuss the Cauchy problem for the Dolbeault cohomology in a domain of C n with data on a part of the boundary. In this setting we introduce the concept of a Carleman function which proves useful in the study of uniqueness. Apart from an abstract framework we show explicit Carleman formulas for the Dolbeault cohomology.
T3  - Preprint - (1998) 10 
KW  - ∂-operator
KW  - cohomology
KW  - integral formulas
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25224
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - On boundary value problems for elliptic equations
Y1  - 1999
SN  - 0002-3264
SN  - 0869-5652
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - On a paper of Krupchyk, Tarkhanov, and Tuomela
T3  - Preprint - (2008) 05 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30325
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - On a paper of Krupchyk, Tarkhanov, and Tuomela
N2  - We compare the above-mentioned article with the content of a previous publication
Y1  - 2009
UR  - http://www.sciencedirect.com/science/journal/00221236
U6  - https://doi.org/10.1016/j.jfa.2008.07.024
SN  - 0022-1236
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - On a paper of Krupchyk, Tarkhanov and Tuomela
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2008
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Hovhannisyan, A. H.
A1  - Schulze, Bert-Wolfgang
T1  - On a method for solution of the ordinary differential equations connected with Huygens' equations
T3  - Preprint - (2010) 01 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-45381
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - Nonstationary problems for equations of Borel-Fuchs type
N2  - In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out.
T3  - Preprint - (1997) 11 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24973
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Nonstationary problems for equations of Borel-Fuchs type
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 11
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Nonstationary problems for Borel-Fuchs type equations
Y1  - 1997
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Noncommutative Analysis and High-Frequency Asymptotics
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Noncommutative analysis : main ideas, definitions, and theorems
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - New algebras of boundary value problems for elliptic pseudodifferential operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Mixed problems and edge calculus : symbol structures
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - De Donno, Giuseppe
A1  - Schulze, Bert-Wolfgang
T1  - Meromorphic symbolic structures for boundary value problems on manifolds with edges
N2  - We investigate the ideal of Green and Mellin operators with asymptotics 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.
Y1  - 2006
UR  - http://www3.interscience.wiley.com/cgi-bin/jhome/60500208
U6  - https://doi.org/10.1002/mana.200310366
SN  - 0025-584X
ER  - 
TY  - BOOK
A1  - De Donno, G.
A1  - Schulze, Bert-Wolfgang
T1  - Meromorphic symbolic structures for boundary value problems on manifolds with edges
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - De Donno, G.
A1  - Schulze, Bert-Wolfgang
T1  - Meromorphic symbolic structures for boundary value problems on manifolds with edges
N2  - 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.
T3  - Preprint - (2003) 10 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26570
ER  - 
TY  - JOUR
A1  - Dines, Nicoleta
A1  - Schulze, Bert-Wolfgang
T1  - Mellin-edge representations of elliptic operators
N2  - 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 A(s) in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of A(s) as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices P-s of A(s) interpreted as Mellin-edge representations of P. Copyright (c) 2005 John Wiley & Sons, Ltd
Y1  - 2005
SN  - 0170-4214
ER  - 
TY  - INPR
A1  - Dines, Nicoleta
A1  - Schulze, Bert-Wolfgang
T1  - Mellin-edge representations of elliptic operators
N2  - 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.
T3  - Preprint - (2003) 18 
KW  - Pseudo-differential operators
KW  - edge algebra
KW  - ellipticity with interface conditions
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26627
ER  - 
TY  - JOUR
A1  - Schrohe, Elmar
A1  - Schulze, Bert-Wolfgang
T1  - Mellin quantization in the cone calculus for Boutet de Monvelïs algebra
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Lyu, Xiaojing
A1  - Schulze, Bert-Wolfgang
T1  - Mellin Operators in the Edge Calculus
JF  - Complex analysis and operator theory
N2  - A manifold M with smooth edge Y is locally near Y modelled on X-Delta x Omega for a cone X-Delta := ( (R) over bar (+) x X)/({0} x X) where Xis a smooth manifold and Omega subset of R-q an open set corresponding to a chart on Y. Compared with pseudo-differential algebras, based on other quantizations of edge-degenerate symbols, we extend the approach with Mellin representations on the r half-axis up to r = infinity, the conical exit of X-boolean AND = R+ x X (sic) (r, x) at infinity. The alternative description of the edge calculus is useful for pseudo-differential structures on manifolds with higher singularities.
KW  - Edge degenerate operators
KW  - Mellin and Green operators edge symbols
Y1  - 2016
U6  - https://doi.org/10.1007/s11785-015-0511-6
SN  - 1661-8254
SN  - 1661-8262
VL  - 10
SP  - 965
EP  - 1000
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Schrohe, Elmar
A1  - Schulze, Bert-Wolfgang
T1  - Mellin operators in a pseudodifferential calculus for boundary value problems on manifolds with edges
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Schrohe, Elmar
A1  - Schulze, Bert-Wolfgang
T1  - Mellin and Green symbols for boundary value problems on manifolds with edges
Y1  - 1999
ER  - 
TY  - BOOK
A1  - Dines, Nicoleta
A1  - Schulze, Bert-Wolfgang
T1  - Melin-edges representations of elliptic operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Manifolds with isolated singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - Long-time asymptotics with geometric singularities in the spatial variables
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - Long-time asymptotics with geometric singularities in the spatial variables
N2  - Content: Introduction 1 Anisotropic operators in a cylinder with a conical base 1.1 Manifolds with conical singularities and opertors of Fuchs type 1.2 Typical operators and symbol structures 2 Weighted wedge Sobolev spaces and edge asymptotics 2.1 Discrete edge asymptotics 2.2 Continuos edge asymptotics with discrete limit at infinity 2.3 Calculus with operator valued symbols 3 Corner asymptotics at infinity 3.1 The structure of singular functions 3.2 Operators with trace and potential conditions 3.3 Asymptotics and (anisotropic) elliptic regularity
T3  - Preprint - (2000) 17 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25824
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Localization Problem in Index Theory of Elliptic Operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Localization problem in index theory of elliptic operators
N2  - 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.
T3  - Preprint - (2001) 34 
KW  - elliptic operators
KW  - index theory
KW  - surgery
KW  - relative index
KW  - manifold with singularities
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26175
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Localization (surgery) in elliptic theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Lefschetz theory on manifolds with edges : introduction
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 08
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Lefschetz theory on manifolds with edges : introduction
N2  - The aim of this book is to develop the Lefschetz fixed point theory for elliptic complexes of pseudodifferential operators on manifolds with edges. The general Lefschetz theory contains the index theory as a special case, while the case to be studied is much more easier than the index problem. The main topics are: - The calculus of pseudodifferential operators on manifolds with edges, especially symbol structures (inner as well as edge symbols). - The concept of ellipticity, parametrix constructions, elliptic regularity in Sobolev spaces. - Hodge theory for elliptic complexes of pseudodifferential operators on manifolds with edges. - Development of the algebraic constructions for these complexes, such as homotopy, tensor products, duality. - A generalization of the fixed point formula of Atiyah and Bott for the case of simple fixed points. - Development of the fixed point formula also in the case of non-simple fixed points, provided that the complex consists of diferential operarators only. - Investigation of geometric complexes (such as, for instance, the de Rham complex and the Dolbeault complex). Results in this direction are desirable because of both purely mathe matical reasons and applications in natural sciences.
N2  - Ziel des Buches ist es, die Lefschetz-Theorie der Fixpunkte für elliptische Komplexe von Pseudodifferentialoperatoren auf Mannigfaltigkeiten mit Kanten zu gewinnen. Die allgemeine Lefschetz-Theorie enthält die Index-Theorie als Spezialfall, aber der Fall, den wir analysieren werden, ist viel leichter als das Index-Problem. Ergebnisse in dieser Richtung sind wünschenswert, einerseits aus innermathematischen Gründen, aber auch im Hinblick auf Anwendungen in den Naturwissenschaften.
T3  - Preprint - (1997) 08 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24948
ER  - 
TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Schulze, Bert-Wolfgang
A1  - Wong, M. W.
T1  - Iterative properties of pseudo-differential operators on edge spaces
JF  - Journal of pseudo-differential operators and applications
N2  - Pseudo-differential operators with twisted symbolic estimates play a large role in the calculus on manifolds with edge singularities. We study here aspects of the underlying abstract concept and establish a new result on iteration of quantizations.
KW  - Pseudo-differential operators
KW  - Twisted symbolic estimates
KW  - Quantizations
Y1  - 2014
U6  - https://doi.org/10.1007/s11868-014-0100-x
SN  - 1662-9981
SN  - 1662-999X
VL  - 5
IS  - 4
SP  - 455
EP  - 479
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - Iterated asymptotics on corner manifolds
Y1  - 1999
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Index defects in elliptic theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Gil, J. B.
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Holomorphic operator-valued symbols for edgedegenerate pseudo-differential operators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Green pseudodifferential operators on manifolds with edges
Y1  - 1998
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Volpato, A.
T1  - Green operators in the edge calculus
N2  - 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.
T3  - Preprint - (2004) 25 
KW  - operators on manifolds with edges
KW  - weighted spaces with asymptotics
KW  - Green and Mellin edge operators
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26846
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Volpato, A.
T1  - Green operators in the edge calculus
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Green integrals on manifolds with cracks
N2  - We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D.
T3  - Preprint - (2000) 12 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25777
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Slapunov, Aleksandr A.
A1  - Tarchanov, Nikolaj N.
T1  - Green integrals on manifolds with cracks
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Burenkov, V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Extension operators for sobolev spaces commuting with a given transform
Y1  - 1998
ER  -