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  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges
N2  - The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.
T3  - Preprint - (2002) 24 
KW  - manifolds with edges
KW  - edge-degenerate operators
KW  - elliptic families
KW  - edge symbol
KW  - Atiyah-Bott obstruction
KW  - parameter-dependent ellipticity
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26415
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges
N2  - Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.
T3  - Preprint - (2002) 15 
KW  - exterior tensor product
KW  - edge-degenerate operators
KW  - elliptic families
KW  - conormal symbol
KW  - Atiyah-Bott obstruction
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26335
ER  -