TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Schulze, Bert-Wolfgang
T1  - Weighted spaces on corner manifolds
JF  - Complex variables and elliptic equations
N2  - We study spaces on manifolds with double weights and iterated discrete and continuous asymptotics, and their relationship with corner pseudo-differential operators.
KW  - manifolds with corners
KW  - iterated asymptotics
KW  - operators with corner symbols
KW  - 35J70
KW  - 47G30
KW  - 58J40
Y1  - 2014
U6  - https://doi.org/10.1080/17476933.2013.876416
SN  - 1747-6933
SN  - 1747-6941
VL  - 59
IS  - 12
SP  - 1706
EP  - 1738
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Mahmoudi, Mahdi Hedayat
A1  - Schulze, Bert-Wolfgang
T1  - Volterra operators in the edge-calculus
JF  - Analysis and Mathematical Physics
N2  - We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).
KW  - Volterra operator
KW  - Anisotropic pseudo-differential operators
KW  - Edge calculus
KW  - Operator-valued symbols of Mellin type
Y1  - 2018
U6  - https://doi.org/10.1007/s13324-018-0238-4
SN  - 1664-2368
SN  - 1664-235X
VL  - 8
IS  - 4
SP  - 551
EP  - 570
PB  - Springer
CY  - Basel
ER  - 
TY  - BOOK
A1  - Buchholz, Thilo
A1  - Schulze, Bert-Wolfgang
T1  - Volterra operators and parabolicity : anisotropic pseudo-differential operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1998
VL  - 1998, 11
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Qin, Yuming
T1  - Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - Transmission algebras on singular spaces with components of different dimensions
Y1  - 1995
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The zaremba problem with singular interfaces as a corner boundary value problem
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem with singular interfaces as a corner boundary value problem
JF  - Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis
N2  - 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 subset of 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 Bull. Sci. Math. ( to appear). 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.
KW  - Zaremba problem
KW  - corner Sobolev spaces with double weights
KW  - pseudo-differential boundary value problems
Y1  - 2006
U6  - https://doi.org/10.1007/s11118-006-9020-6
SN  - 0926-2601
VL  - 25
SP  - 327
EP  - 369
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - BOOK
A1  - Dines, Nicoleta
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem in edge sobolev spaces
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - The variable discrete asymptotics in pseudo-differential boundary value problems II
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - The variable discrete asymptotics in pseudo-differential boundary value problems II
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - The variable discrete asymptotics in pseudo-differential boundary value problems
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - The trajectory attractor for a nonlinear elliptic system in a cylindrical domain with piecewise smooth boundary
JF  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - The structure of operators on manifolds with polyhedral singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The Riemann-Roch theorem for manifolds with conical singularities
Y1  - 1999
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The Rieman-Roch theorem for manifolds with conical singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 18
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The relative index for corner singularities
N2  - We study pseudo-differential operators on a cylinder R x B where B has conical singularities. Configurations of that kind are the local model of corner singularities with cross section B. Operators in our calculus are assumed to have symbols a which are meromorphic in the complex covariable with values in the algebra of all cone operators on B. We show an explicit formula for solutions of the homogeneous equation if a is independent of the axial variable t is an element of R. Each non-bijectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula
Y1  - 2006
UR  - http://www.springerlink.com/content/300422
U6  - https://doi.org/10.1007/s00020-005-1367-3
SN  - 0378-620X
ER  - 
TY  - BOOK
A1  - Martin, Calin-Iulian
A1  - Schulze, Bert-Wolfgang
T1  - The Quantisation of edge symbols
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Wei, Y.
T1  - The Mellin-edge quantisation for corner operators
JF  - Complex analysis and operator theory
N2  - We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold with second order singularities. The typical ingredients come from the "most singular" stratum of which is a second order edge where the infinite transversal cone has a base that is itself a manifold with smooth edge. The resulting operator-valued amplitude functions on the second order edge are formulated purely in terms of Mellin symbols taking values in the edge algebra over . In this respect our result is formally analogous to a quantisation rule of (Osaka J. Math. 37:221-260, 2000) for the simpler case of edge-degenerate symbols that corresponds to the singularity order 1. However, from the singularity order 2 on there appear new substantial difficulties for the first time, partly caused by the edge singularities of the cone over that tend to infinity.
Y1  - 2014
U6  - https://doi.org/10.1007/s11785-013-0289-3
SN  - 1661-8254
SN  - 1661-8262
VL  - 8
IS  - 4
SP  - 803
EP  - 841
PB  - Springer
CY  - Basel
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - The index problem on manifolds with singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Sternin, Boris Ju.
A1  - Schulze, Bert-Wolfgang
T1  - The index of quantized contact transformations on manifolds with conical singularities
Y1  - 1999
SN  - 0002-3264
SN  - 0869-5652
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - The index of quantized contact transformations on manifolds with conical singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1998
VL  - 1998, 16
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The index of higher order operators on singular surfaces
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1998
VL  - 1998, 03
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The index of elliptic operators on manifolds with cups
Y1  - 1997
ER  - 
TY  - BOOK
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The index of elliptic operators on manifolds with conical points
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 24
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The index of elliptic operators on manifolds with conical points
Y1  - 1999
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
T1  - The homotopy classification and the index of boundary value problems for general elliptic operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - CHAP
A1  - Rungrottheera, Wannarut
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - The edge calculus of singularity order >3
T2  - Journal of nonlinear and convex analysis : an international journal
N2  - We study Mellin pseudo-differential algebras on singular straight cones and manifolds with singularity of order >= 3. Those are necessary to express parametrices of elliptic differential operators with a corresponding cornerdegenerate behavior, and we obtain regularity in weighted spaces.
KW  - Pseudo-differential algebras
KW  - symbols
KW  - singular manifolds
KW  - Mellin
KW  - operator calculus
Y1  - 2020
SN  - 1345-4773
SN  - 1880-5221
VL  - 21
IS  - 2
SP  - 387
EP  - 401
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Habal, Nadia
A1  - Schulze, Bert-Wolfgang
T1  - The edge algebra structure of the Zaremba problem
JF  - Journal of pseudo-differential operators and applications
N2  - We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.
Y1  - 2014
U6  - https://doi.org/10.1007/s11868-013-0088-7
SN  - 1662-9981
SN  - 1662-999X
VL  - 5
IS  - 1
SP  - 69
EP  - 155
PB  - Springer
CY  - Basel
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - The edge algebra structure of boundary value problems
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  - The Conormal symbolic structure of corner boundary value problems
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - The Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - The Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singularities
Y1  - 1999
SN  - 0002-3264
SN  - 0869-5652
ER  - 
TY  - BOOK
A1  - Calvo, D.
A1  - Martin, Calin-Iulian
A1  - Schulze, Bert-Wolfgang
T1  - Symbolic Structures on Corner Manifolds
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Symbolic calcullus for boundary value problems on manifolds with edges
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Symbol algebra for manifolds with cuspidal singularities
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  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Surgery and the relative index theorem for families of elliptic operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Structure rings of singularities and differential equations
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Spectral boundary value problems and elliptic equations on singular manifolds
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Spectral boundary value problems and elliptic equations on manifolds with singularities
Y1  - 1999
SN  - 0002-3264
SN  - 0869-5652
ER  - 
TY  - BOOK
A1  - Jaiani, George V.
A1  - Schulze, Bert-Wolfgang
T1  - Some degenerate elliptic systems and applications to cousped plates
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - Singular degenerate operators
JF  - Applicable analysis : an international journal
N2  - We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.
KW  - Operators on singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - parametrices of elliptic operators
Y1  - 2017
U6  - https://doi.org/10.1080/00036811.2017.1336546
SN  - 0003-6811
SN  - 1563-504X
VL  - 96
IS  - 14
SP  - 2434
EP  - 2456
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - GEN
A1  - Flad, Heinz-Jürgen
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Singular analysis and coupled cluster theory
N2  - The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to shortrange correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 302 
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102306
SP  - 31530
EP  - 31541
ER  - 
TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Singular analysis and coupled cluster theory
JF  - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2  - The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to short-range correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.
Y1  - 2015
U6  - https://doi.org/10.1039/c5cp01183c
SN  - 1463-9076
SN  - 1463-9084
VL  - 17
IS  - 47
SP  - 31530
EP  - 31541
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Resurgent analysis in the theory of differential equations with singularities
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Resurgent analysis and differential equations with singularities
Y1  - 1994
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Slapunov, Aleksandr A.
A1  - Tarchanov, Nikolaj N.
T1  - Regularisation of mixed boundary problems
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Reduction of orders in boundary value problems without transmission property
N2  - 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
Y1  - 2004
SN  - 0025-5645
ER  - 
TY  - BOOK
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Reduction of Orders in Boundary Value Problems without the Transmission Proberty
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Quantizational of canonical transformations on manifolds with conical singularities
Y1  - 1999
SN  - 0002-3264
SN  - 0869-5652
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Quantization of Lagrangian modules
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Quantization and the wave packet transform
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
A1  - Schulze, Bert-Wolfgang
T1  - Pseudodifferential operators on manifolds with singularities and localization
Y1  - 2005
SN  - 1064-5624
ER  - 
TY  - JOUR
A1  - Nazajkinskij, Vladimir E.
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
A1  - Schulze, Bert-Wolfgang
T1  - Pseudodifferential operators on manifolds with edges
Y1  - 2004
SN  - 1064-5624
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Pseudodifferential operators on manifolds with corners
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  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Pseudodifferential Operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Pseudodifferential calculus on manifolds with singular points
Y1  - 1998
SN  - 1311- 0454
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Pseudodifferential boundary value problems with global projection conditions
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Egorov, Jurij V.
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential operators, singularities, applicatons
T3  - Operator theory
Y1  - 1997
SN  - 3-7643-5484-4
VL  - 93
PB  - Birkhäuser
CY  - Basel
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential operators, ellipticity and asymptotics on manifolds with edges
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Dorschfeldt, Christoph
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential operators with operator-valued symbols in the Mellin-edge-approach
Y1  - 1994
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential Crack Theory
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
T1  - Pseudo-differential calculus on Manifolds with geometric singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Dorschfeldt, Christoph
A1  - Grieme, Ulrich
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential calculus in the Fourieredge approach on non-compact manifolds
Y1  - 1997
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential calculus and applications to non-smooth configurations
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 1999
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential boundary value problems, conical singularities, and asymptotics
T3  - Mathematical topics
Y1  - 1994
SN  - 3-05-501597-5
VL  - 4
PB  - Akad.-Verl.
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Chang, D. -C.
A1  - Viahmoudi, M. Hedayat
A1  - Schulze, Bert-Wolfgang
T1  - PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.
KW  - Pseudo-differential operators
KW  - boundary value problems
KW  - operator valued symbols
KW  - Fourier transform
Y1  - 2016
SN  - 1345-4773
SN  - 1880-5221
VL  - 17
SP  - 1889
EP  - 1937
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Parametrices of mixed elliptic problems
N2  - 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
Y1  - 2004
SN  - 0025-584X
ER  - 
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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  -