TY - INPR A1 - Rabinovich, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A calculus of boundary value problems in domains with Non-Lipschitz Singular Points N2 - The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points. T3 - Preprint - (1997) 09 KW - pseudodifferential operators KW - boundary value problems KW - manifolds with cusps Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24957 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 - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A general index formula on tropic manifolds with conical points N2 - We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points. T3 - Preprint - (1999) 15 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25501 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Lefschetz fixed point formula in the relative elliptic theory N2 - A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology. T3 - Preprint - (1998) 01 KW - elliptic complexes KW - relative cohomology KW - Lefschetz number Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25159 ER - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A remark on the index of symmetric operators N2 - We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol. T3 - Preprint - (1998) 04 KW - manifolds with singularities KW - differential operators KW - index KW - 'eta' invariant Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25169 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Asymptotics of solutions to elliptic equatons on manifolds with corners N2 - We show an explicit link between the nature of a singular point and behaviour of the coefficients of the equation, under which formal asymptotic expansions are still available. T3 - Preprint - (2000) 05 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25716 ER - TY - INPR A1 - Rabinovich, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Boundary value problems in cuspidal wedges N2 - The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges. T3 - Preprint - (1998) 24 KW - pseudodifferential operators KW - boundary value problems KW - manifolds with edges Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25363 ER - TY - INPR A1 - Rabinovich, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Boundary value problems in domains with corners N2 - We describe Fredholm boundary value problems for differential equations in domains with intersecting cuspidal edges on the boundary. T3 - Preprint - (1999) 19 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25552 ER - TY - JOUR A1 - Rabinovich, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Boundary value problems in oscillating cuspidal wedges N2 - The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges Y1 - 2004 SN - 0035-7596 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 -