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  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Calculus on a Manifold with Edge and Boundary
JF  - Complex analysis and operator theory
N2  - We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel’s algebra (Acta Math 126:11–51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.
KW  - algebra
KW  - Mellin quantization
Y1  - 2019
U6  - https://doi.org/10.1007/s11785-018-0800-y
SN  - 1661-8254
SN  - 1661-8262
VL  - 13
IS  - 6
SP  - 2627
EP  - 2670
PB  - Springer
CY  - Basel
ER  -