TY  - INPR
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A calculus of boundary value problems in domains with Non-Lipschitz Singular Points
N2  - The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.
T3  - Preprint - (1997) 09 
KW  - pseudodifferential operators
KW  - boundary value problems
KW  - manifolds with cusps
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24957
ER  - 
TY  - BOOK
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - A calculus of boundary value problems in domains with Non-Lipschitz singular points
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1997
VL  - 1997, 09
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A general index formula on toric manifolds with conical point
Y1  - 2001
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A general index formula on tropic manifolds with conical points
N2  - We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.
T3  - Preprint - (1999) 15 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25501
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Lefschetz fixed point formula in the relative elliptic theory
N2  - A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology.
T3  - Preprint - (1998) 01 
KW  - elliptic complexes
KW  - relative cohomology
KW  - Lefschetz number
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25159
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - A Lefschetz fixed point theorem for manifolds with conical singularities
N2  - We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points.
T3  - Preprint - (1997) 20 
KW  - elliptic operator
KW  - Fredholm property
KW  - conical singularities
KW  - pseudo-diferential operators
KW  - Lefschetz fixed point formula
KW  - regularizer
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25073
ER  - 
TY  - JOUR
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - A new approach to the second order edge calculus
JF  - Journal of pseudo-differential operators and applications
N2  - We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
KW  - Operators on singular manifolds
KW  - Mellin transform
KW  - Stratified spaces
KW  - Ellipticity and parametrices
Y1  - 2018
U6  - https://doi.org/10.1007/s11868-017-0191-2
SN  - 1662-9981
SN  - 1662-999X
VL  - 9
IS  - 2
SP  - 265
EP  - 300
PB  - Springer
CY  - Basel
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A remark on the index of symmetric operators
N2  - We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.
T3  - Preprint - (1998) 04 
KW  - manifolds with singularities
KW  - differential operators
KW  - index
KW  - 'eta' invariant
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25169
ER  - 
TY  - BOOK
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - A remark on the index of symmetric operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1998
VL  - 1998, 04
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Nazaikinskii, Vladimir
A1  - Sternin, Boris
T1  - A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators
N2  - For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space.
T3  - Preprint - (1998) 19 
KW  - elliptic operator
KW  - Fredholm property
KW  - conical singularities
KW  - pseudodiferential operators
KW  - Lefschetz fixed point formula
KW  - regularizer
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25296
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - A semiclassical quantization on manifolds with singularities and the Lefschetz formula for elliptic operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik
Y1  - 1998
VL  - 1998, 19
PB  - Univ.
CY  - Potsdam
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  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Demuth, Michael
A1  - Albeverio, Sergio
A1  - Schrohe, Elmar
T1  - Advances in Partial differential equations
Y1  - 2001
PB  - Birkhäuser
CY  - Basel
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
T1  - An algebra of boundary value problems not requiring Shapiro-Lopatinskij conditions
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  - An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions
N2  - We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.
T3  - Preprint - (1999) 24 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25596
ER  - 
TY  - INPR
A1  - Maniccia, L.
A1  - Schulze, Bert-Wolfgang
T1  - An algebra of meromorphic corner symbols
N2  - Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.
T3  - Preprint - (2002) 18 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26360
ER  - 
TY  - BOOK
A1  - Maniccia, L.
A1  - Schulze, Bert-Wolfgang
T1  - An algebra of meromorphic corner symbols
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  - An operator algebra on manifolds with cusp type singularities
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Analysis on regular corner spaces
JF  - The journal of geometric analysis
N2  - We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.
KW  - Boutet de Monvel's calculus
KW  - Pseudo-differential operators
KW  - Singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - Parametrices of elliptic operators
KW  - Kegel space
Y1  - 2021
U6  - https://doi.org/10.1007/s12220-021-00614-3
SN  - 1050-6926
SN  - 1559-002X
VL  - 31
IS  - 9
SP  - 9199
EP  - 9240
PB  - Springer
CY  - New York
ER  - 
TY  - BOOK
A1  - Fedosov, Boris V.
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Analytic index formulas for elliptic corner operators
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  -