TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Wei, Ya-wei
T1  - Edge-boundary problems with singular trace conditions
N2  - The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (sigma(psi), sigma(partial derivative)), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary, we have a third symbolic component, namely, the edge symbol sigma(boolean AND), referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions 'in integral form' there may exist singular trace conditions, investigated in Kapanadze et al., Internal Equations and Operator Theory, 61, 241-279, 2008 on 'closed' manifolds with edge. Here, we concentrate on the phenomena in combination with boundary conditions and edge problem.
Y1  - 2009
UR  - http://www.springerlink.com/content/100233
U6  - https://doi.org/10.1007/s10455-008-9143-7
SN  - 0232-704X
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  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The index of elliptic operators on manifolds with cups
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Coordinate invariance of the wedge Sobolev spaces = Wedge Sobelev spaces
BT  - Wedge Sobolev spaces
Y1  - 1996
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Elliptic complexes of pseudodifferential operators on manifolds with edges
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Ellipticity and parametrices on manifolds with cuspidal edges
Y1  - 1999
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  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - The Riemann-Roch theorem for manifolds with conical singularities
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Green pseudodifferential operators on manifolds with edges
Y1  - 1998
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  - 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  - 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  - 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  - 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  - On the index of elliptic operators on manifolds with conical singularities
Y1  - 1999
SN  - 0002-3264
SN  - 0869-5652
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  - 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 the index of differential operators on manifolds with conical singularities
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - An operator algebra on manifolds with cusp type singularities
Y1  - 1998
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  - 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  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
A1  - Satalov, Viktor E.
T1  - Differential equations on manifolds with singularities in classes of resurgent functions
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Edge operators with conditions of Toeplitz type
N2  - Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of 2 X 2-block matrix operators with trace and potential operators on the edges. The picture is similar to the pseudodifferential analysis of boundary-value problems. The extra conditions satisfy an analogue of the Shapiro-Lopatinskij condition, provided a topological obstruction for the elliptic edge-degenerate operator in the upper left corner vanishes; this is an analogue of a condition of Atiyah and Bott in boundary-value problems. In general, however, we need global projection data, similarly to global boundary conditions, known for Dirac operators or other geometric operators. The present paper develops a new calculus with global projection data for operators on manifolds with edges. In particular, we show the Fredholm property in a suitable scale of spaces and construct parametrices within the calculus
Y1  - 2006
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Boundary value problems with global projection conditions
N2  - Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved
Y1  - 2004
SN  - 0022-1236
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Elliptic complexes on manifolds with boundary
JF  - The journal of geometric analysis
N2  - We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.
KW  - Elliptic complexes
KW  - Manifolds with boundary
KW  - Atiyah-Bott obstruction
KW  - Toeplitz-type pseudodifferential operators
Y1  - 2018
U6  - https://doi.org/10.1007/s12220-018-0014-6
SN  - 1050-6926
SN  - 1559-002X
VL  - 29
IS  - 1
SP  - 656
EP  - 706
PB  - Springer
CY  - New York
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  - Boundary value problems and edges pseudo-differential operators
Y1  - 1997
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  - Pseudo-differential operators, ellipticity and asymptotics on manifolds with edges
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - Transmission algebras on singular spaces with components of different dimensions
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - Operator algebras with symbol hierarchies on manifolds with singularities
Y1  - 2001
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  - 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  - JOUR
A1  - Schulze, Bert-Wolfgang
T1  - Iterated asymptotics on corner manifolds
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Schrohe, Elmar
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems in Boutet de Monvel's algebra for manifolds with conical singularities II
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Schrohe, Elmar
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems in Boutet de Monvelïs algebra for manifolds with conical singularities I
Y1  - 1994
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  - Schrohe, Elmar
A1  - Schulze, Bert-Wolfgang
T1  - A symbol algebra for pseudodifferential boundary value problems on manifolds with edges
Y1  - 1997
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  - 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  - 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  - 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  - 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  - 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  - JOUR
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Boundary value problems in oscillating cuspidal wedges
N2  - The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges
Y1  - 2004
SN  - 0035-7596
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  - 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  - 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  - 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  -