@unpublished{SchulzeSterninShatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor}, title = {On the index of differential operators on manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24965}, year = {1997}, abstract = {The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.}, language = {en} } @unpublished{SchulzeNazaikinskiiSternin1998, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris}, title = {The index of quantized contact transformations on manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25276}, year = {1998}, abstract = {The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.}, language = {en} } @unpublished{PolkovnikovTarkhanov2017, author = {Polkovnikov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {A Riemann-Hilbert problem for the Moisil-Teodorescu system}, volume = {6}, number = {3}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-397036}, pages = {31}, year = {2017}, abstract = {In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations for a function u with values in R^3 subject to a nonhomogeneous condition (u,v)_x = u_0 on the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.}, language = {en} }