@unpublished{SchulzeNazaikinskiiSternin1999, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir E. and Sternin, Boris}, title = {On the homotopy classification of elliptic operators on manifolds with singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25574}, year = {1999}, abstract = {We study the homotopy classification of elliptic operators on manifolds with singularities and establish necessary and sufficient conditions under which the classification splits into terms corresponding to the principal symbol and the conormal symbol.}, language = {en} } @article{SchulzeSterninSatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Nonstationary problems for Borel-Fuchs type equations}, year = {1997}, language = {en} } @unpublished{NazaikinskiiSchulzeSternin2002, author = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Surgery and the relative index theorem for families of elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26300}, year = {2002}, abstract = {We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems.}, language = {en} } @unpublished{NazaikinskiiSchulzeSternin1999, author = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Quantization and the wave packet transform}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25447}, year = {1999}, language = {en} } @unpublished{SchulzeSavinSternin1999, author = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris}, title = {Elliptic operators in subspaces and the eta invariant}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25496}, year = {1999}, abstract = {The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.}, language = {en} } @book{NazajkinskijSavinSchulzeetal.2002, author = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic theory on manifolds with nonisolated singularities : 4 obstructions to elliptic problems on manifolds with edges}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {21 S.}, year = {2002}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2003, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Differential operators on manifolds with singularities : analysis and topology : Chapter 3: Eta invariant and the spectral flow}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26595}, year = {2003}, abstract = {Contents: Chapter 3: Eta Invariant and the Spectral Flow 3.1. Introduction 3.2. The Classical Spectral Flow 3.2.1. Definition and main properties 3.2.2. The spectral flow formula for periodic families 3.3. The Atiyah-Patodi-Singer Eta Invariant 3.3.1. Definition of the eta invariant 3.3.2. Variation under deformations of the operator 3.3.3. Homotopy invariance. Examples 3.4. The Eta Invariant of Families with Parameter (Melrose's Theory) 3.4.1. A trace on the algebra of parameter-dependent operators 3.4.2. Definition of the Melrose eta invariant 3.4.3. Relationship with the Atiyah-Patodi-Singer eta invariant 3.4.4. Locality of the derivative of the eta invariant. Examples 3.5. The Spectral Flow of Families of Parameter-Dependent Operators 3.5.1. Meromorphic operator functions. Multiplicities of singular points 3.5.2. Definition of the spectral flow 3.6. Higher Spectral Flows 3.6.1. Spectral sections 3.6.2. Spectral flow of homotopies of families of self-adjoint operators 3.6.3. Spectral flow of homotopies of families of parameter-dependent operators 3.7. Bibliographical Remarks}, language = {en} } @unpublished{NazaikinskiiSavinSchulzeetal.2003, author = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Differential operators on manifolds with singularities : analysis and topology : Chapter 4: Pseudodifferential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26587}, year = {2003}, abstract = {Contents: Chapter 4: Pseudodifferential Operators 4.1. Preliminary Remarks 4.1.1. Why are pseudodifferential operators needed? 4.1.2. What is a pseudodifferential operator? 4.1.3. What properties should the pseudodifferential calculus possess? 4.2. Classical Pseudodifferential Operators on Smooth Manifolds 4.2.1. Definition of pseudodifferential operators on a manifold 4.2.2. H{\"o}rmander's definition of pseudodifferential operators 4.2.3. Basic properties of pseudodifferential operators 4.3. Pseudodifferential Operators in Sections of Hilbert Bundles 4.3.1. Hilbert bundles 4.3.2. Operator-valued symbols. Specific features of the infinite-dimensional case 4.3.3. Symbols of compact fiber variation 4.3.4. Definition of pseudodifferential operators 4.3.5. The composition theorem 4.3.6. Ellipticity 4.3.7. The finiteness theorem 4.4. The Index Theorem 4.4.1. The Atiyah-Singer index theorem 4.4.2. The index theorem for pseudodifferential operators in sections of Hilbert bundles 4.4.3. Proof of the index theorem 4.5. Bibliographical Remarks}, language = {en} } @article{NazajkinskijSavinSterninetal.2005, author = {Nazajkinskij, Vladimir E. and Savin, Anton and Sternin, Boris Ju. and Schulze, Bert-Wolfgang}, title = {On the index of elliptic operators on manifolds with edges}, year = {2005}, abstract = {Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables}, language = {en} } @unpublished{SchulzeSterninShatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor}, title = {Operator algebras on singular manifolds. I}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25011}, year = {1997}, language = {en} }