@unpublished{SchulzeSterninSavin1999, author = {Schulze, Bert-Wolfgang and Sternin, Boris and Savin, Anton}, title = {The homotopy classification and the index of boundary value problems for general elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25568}, year = {1999}, abstract = {We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.}, language = {en} } @unpublished{NazaikinskiiSternin1999, author = {Nazaikinskii, Vladimir E. and Sternin, Boris}, title = {Surgery and the relative index in elliptic theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25538}, year = {1999}, abstract = {We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.}, language = {en} }