TY  - INPR
A1  - Kytmanov, Alexander
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Holomorphic Lefschetz formula for manifolds with boundary
N2  - The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M -> M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschtz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah-Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschtz formula on a compact complex manifold with boundary
T3  - Preprint - (2002) 17 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26354
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Anisotropic edge problems
N2  - We investigate elliptic pseudodifferential operators which degenerate in an anisotropic way on a submanifold of arbitrary codimension. To find Fredholm problems for such operators we adjoint to them boundary and coboundary conditions on the submanifold.The algebra obtained this way is a far reaching generalisation of Boutet de Monvel's algebra of boundary value problems with transmission property. We construct left and right regularisers and prove theorems on hypoellipticity and local solvability.
T3  - Preprint - (2002) 09 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26280
ER  -