@unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The index of higher order operators on singular surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25127}, year = {1998}, abstract = {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of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1997, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {On the index formula for singular surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25116}, year = {1997}, abstract = {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 In this paper we clarify the meaning of the additional terms for differential operators.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A remark on the index of symmetric operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169}, year = {1998}, abstract = {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.}, language = {en} }