TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
A1  - Vasilevski, Nikolai
T1  - Microlocal analysis of the Bochner-Martinelli integral
N2  - In order to characterise the C*-algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in Cn, we compute its principal symbol. We show then that the Szegö projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral.
T3  - Preprint - (2005) 25 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30012
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On the root functions of general elliptic boundary value problems
N2  - We consider a boundary value problem for an elliptic differential operator of order 2m in a domain D ⊂ n. The boundary of D is smooth outside a finite number of conical points, and the Lopatinskii condition is fulfilled on the smooth part of δD. The corresponding spaces are weighted Sobolev spaces H(up s,Υ)(D), and this allows one to define ellipticity of weight Υ for the problem. The resolvent of the problem is assumed to possess rays of minimal growth. The main result says that if there are rays of minimal growth with angles between neighbouring rays not exceeding π(Υ + 2m)/n, then the root functions of the problem are complete in L²(D). In the case of second order elliptic equations the results remain true for all domains with Lipschitz boundary.
T3  - Preprint - (2005) 07a 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29822
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Unitary solutions of partial differential equations
N2  - We give an explicit construction of a fundamental solution for an arbitrary non-degenerate partial differential equation with smooth coefficients.
T3  - Preprint - (2005) 09 
KW  - fundamental solution
KW  - geometric optics approximation
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29852
ER  - 
TY  - INPR
A1  - Krupchyk, K.
A1  - Tarkhanov, Nikolai Nikolaevich
A1  - Tuomela, J.
T1  - Generalised elliptic boundary problems
N2  - For elliptic systems of differential equations on a manifold with boundary, we prove the Fredholm property of a class of boundary problems which do not satisfy the Shapiro-Lopatinskii property. We name these boundary problems generalised elliptic, for they preserve the main properties of elliptic boundary problems. Moreover, they reduce to systems of pseudodifferential operators on the boundary which are generalised elliptic in the sense of Saks (1997).
T3  - Preprint - (2005) 23 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29994
ER  - 
TY  - INPR
A1  - Aizenberg, Lev A.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Stable expansions in homogeneous polynomials
N2  - An expansion for a class of functions is called stable if the partial sums are bounded uniformly in the class. Stable expansions are of key importance in numerical analysis where functions are given up to certain error. We show that expansions in homogeneous functions are always stable on a small ball around the origin, and evaluate the radius of the largest ball with this property.
T3  - Preprint - (2005) 16 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29925
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Boundary value problems with Toeplitz conditions
N2  - We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which serve as domains of pseudodifferential operators and which fit well to the nature of operators.
T3  - Preprint - (2005) 08 
KW  - Pseudodifferential operators
KW  - boundary values problems
KW  - Toeplitz operators
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29837
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Root functions of elliptic boundary problems in domains with conic points of the boundary
N2  - We prove the completeness of the system of eigen and associated functions (i.e., root functions) of an elliptic boundary value problem in a domain whose boundary is a smooth surface away from a finite number of points, each of them possesses a neighbourhood where the boundary is a conical surface.
T3  - Preprint - (2005) 07 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29812
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Operator algebras related to the Bochner-Martinelli Integral
N2  - We describe a general method of computing the square of the singular integral of Bochner-Martinelli. Any explicit formula for the square applies in a familiar way to describe the C*-algebra generated by this integral.
T3  - Preprint - (2005) 04 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29789
ER  -