TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Duality by reproducing kernels
N2  - Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A.
T3  - Preprint - (2001) 26 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26095
ER  - 
TY  - BOOK
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Duality by reproducing kernels
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Prenov, B.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Kernel Spikes of Singular Problems
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Prenov, B.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Kernel spikes of singular problems
N2  - Function spaces with asymptotics is a usual tool in the analysis on manifolds with singularities. The asymptotics are singular ingredients of the kernels of pseudodifferential operators in the calculus. They correspond to potentials supported by the singularities of the manifold, and in this form asymptotics can be treated already on smooth configurations. This paper is aimed at describing refined asymptotics in the Dirichlet problem in a ball. The beauty of explicit formulas highlights the structure of asymptotic expansions in the calculi on singular varieties.
T3  - Preprint - (2001) 36 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26195
ER  - 
TY  - BOOK
A1  - Kytmanov, Alexander M.
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An Asymptotic expansion of the Bochner-Martinelli integral
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgrupe Partielle Differentialgleichun
Y1  - 2001
SN  - 1437-339X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Elliptic problems for the Dolbeault complex
N2  - The inhomogeneous ∂-equations is an inexhaustible source of locally unsolvable equations, subelliptic estimates and other phenomena in partial differential equations. Loosely speaking, for the anaysis on complex manifolds with boundary nonelliptic problems are typical rather than elliptic ones. Using explicit integral representations we assign a Fredholm complex to the Dolbeault complex over an arbitrary bounded domain in C up(n).
T3  - Preprint - (2001) 13 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25979
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  -