TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - The index of higher order operators on singular surfaces N2 - The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol. T3 - Preprint - (1998) 03 KW - manifolds with singularities KW - differential operators KW - index KW - 'eta' invariant KW - monodromy matrix Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25127 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 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Spectral boundary value problems and elliptic equations on singular manifolds N2 - For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established. T3 - Preprint - (1997) 36 KW - APS problem KW - spectral resolution KW - nonhomogeneous boundary value problems KW - Fredholm property Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25147 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - On general boundary value problems for elliptic equations N2 - We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved. T3 - Preprint - (1997) 35 KW - elliptic boundary value problems KW - Atiyah-Bott condition KW - Calderón projections KW - Cauchy Riemann operator KW - Euler operator Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25138 ER - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - On the index formula for singular surfaces N2 - In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators. T3 - Preprint - (1997) 31 KW - manifolds with singularities KW - differential operators KW - index KW - 'eta' invariant KW - monodromy matrix Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25116 ER - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - The index of elliptic operators on manifolds with conical points N2 - For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero. T3 - Preprint - (1997) 24 KW - manifolds with singularities KW - pseudodifferential operators KW - elliptic operators KW - index Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25096 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Quantization of symplectic transformations on manifolds with conical singularities N2 - The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated. T3 - Preprint - (1997) 23 KW - manifolds with conical singularities KW - symplectic (canonical) transformations KW - quantization KW - Mellin transform Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25084 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - A Lefschetz fixed point theorem for manifolds with conical singularities N2 - We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points. T3 - Preprint - (1997) 20 KW - elliptic operator KW - Fredholm property KW - conical singularities KW - pseudo-diferential operators KW - Lefschetz fixed point formula KW - regularizer Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25073 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Operator algebras on singular manifolds. IV, V T3 - Preprint - (1997) 19 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25062 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - The Riemann-Roch theorem for manifolds with conical singularities N2 - The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points. T3 - Preprint - (1997) 18 KW - manifolds with singularities KW - elliptic operators KW - divisors Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25051 ER -