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  - INPR
A1  - Buchholz, Thilo
A1  - Schulze, Bert-Wolfgang
T1  - Volterra operators and parabolicity : anisotropic pseudo-differential operators
N2  - Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.
T3  - Preprint - (1998) 11 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25231
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  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Qin, Yuming
T1  - Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity
N2  - In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.
T3  - Preprint - (2005) 13 
KW  - exponential stability
KW  - semiprocess
KW  - absorbing set
KW  - C0−semigroup
KW  - uniform compact attractor
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29892
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  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
N2  - Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.
T3  - Preprint - (2003) 03 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26510
ER  - 
TY  - INPR
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem with singular interfaces as a corner boundary value problem
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 ⊂ 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.
T3  - Preprint - (2004) 26 
KW  - Zaremba problem
KW  - corner Sobolev spaces with double weights
KW  - pseudodifferential boundary value problems
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26855
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  - INPR
A1  - Dines, Nicoleta
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem in edge Sobolev spaces
N2  - Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.
T3  - Preprint - (2003) 13 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26615
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  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - The structure of operators on manifolds with polyhedral singularities
N2  - We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.
T3  - Preprint - (2006) 05 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30099
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The Riemann-Roch theorem for manifolds with conical singularities
N2  - The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points.
T3  - Preprint - (1997) 18 
KW  - manifolds with singularities
KW  - elliptic operators
KW  - divisors
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25051
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  - INPR
A1  - Martin, C.-I.
A1  - Schulze, Bert-Wolfgang
T1  - The quantisation of edge symbols
N2  - We investigate operators on manifolds with edges from the point of view of the symbolic calculus induced by the singularities. We discuss new aspects of the quantisation of edge-degenerate symbols which lead to continuous operators in weighted edge spaces.
T3  - Preprint - (2005) 19 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29959
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  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - The iterative structure of corner operators
N2  - We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference “Elliptic and Hyperbolic Equations on Singular Spaces”, October 27 - 31, 2008, at the MSRI, University of Berkeley.
T3  - Preprint - (2008) 08 
KW  - Categories of stratified spaces
KW  - ellipticity of corners operators
KW  - principal symbolic hierarchies
KW  - boundary value problems
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30353
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  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Nazaikinskii, Vladimir
A1  - Sternin, Boris
T1  - The index of quantized contact transformations on manifolds with conical singularities
N2  - The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.
T3  - Preprint - (1998) 16 
KW  - manifolds with conical singularities
KW  - contact transformations
KW  - quantization
KW  - ellipticity
KW  - Fredholm operators
KW  - regularizers
KW  - index formulas
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25276
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  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The index of higher order operators on singular surfaces
N2  - The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.
T3  - Preprint - (1998) 03 
KW  - manifolds with singularities
KW  - differential operators
KW  - index
KW  - 'eta' invariant
KW  - monodromy matrix
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25127
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  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The index of elliptic operators on manifolds with conical points
N2  - For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.
T3  - Preprint - (1997) 24 
KW  - manifolds with singularities
KW  - pseudodifferential operators
KW  - elliptic operators
KW  - index
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25096
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  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Savin, Anton
T1  - The homotopy classification and the index of boundary value problems for general elliptic operators
N2  - We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.
T3  - Preprint - (1999) 20 
KW  - elliptic boundary value problems
KW  - Atiyah-Bott condition
KW  - index theory
KW  - K-theory
KW  - homotopy classification
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25568
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  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - The edge algebra structure of boundary value problems
N2  - Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols.
T3  - Preprint - (2001) 11 
KW  - Boundary value problems
KW  - pseudodifferential operators
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25955
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  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - The conormal symbolic structure of corner boundary value problems
N2  - 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.
T3  - Preprint - (2004) 01 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26662
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  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Symbolic calculus for boundary value problems on manifolds with edges
N2  - Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy of symbols. The symbol structure is responsible or ellipicity and for the nature of parametrices within an algebra of "edge-degenerate" pseudo-differential operators. The edge symbol component of that hierarchy takes values in boundary value problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in this theory, in particular, the contribution with holomorphic operatot-valued Mellin symbols. We establish a calculus in s framework of "twisted homogenity" that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces. We then derive an equivalent representation with a particularly transparent composition behaviour.
T3  - Preprint - (2001) 21 
KW  - pseudo-differential boundary value problems
KW  - operators on manifolds with singularities
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26046
ER  -