TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Savin, Anton
T1  - The homotopy classification and the index of boundary value problems for general elliptic operators
N2  - 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.
T3  - Preprint - (1999) 20 
KW  - elliptic boundary value problems
KW  - Atiyah-Bott condition
KW  - index theory
KW  - K-theory
KW  - homotopy classification
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25568
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Elliptic operators in subspaces and the eta invariant
N2  - 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.
T3  - Preprint - (1999) 14 
KW  - index of elliptic operators in subspaces
KW  - K-theory
KW  - eta-invariant
KW  - mod k index
KW  - Atiyah-Patodi-Singer theory
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25496
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Eta-invariant and Pontrjagin duality in K-theory
N2  - The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.
T3  - Preprint - (2000) 08 
KW  - eta-invariant
KW  - K-theory
KW  - Pontrjagin duality
KW  - linking coefficients
KW  - Atiyah-Patodi-Singer theory
KW  - modulo n index
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25747
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Elliptic operators in odd subspaces
N2  - An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.
T3  - Preprint - (1999) 11 
KW  - index of elliptic operators in subspaces
KW  - K-theory
KW  - eta invariant
KW  - Atiyah-Patodi-Singer theory
KW  - boundary value problems
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25478
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Eta invariant and parity conditions
N2  - We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey.
T3  - Preprint - (2000) 21 
KW  - eta invariant
KW  - parity conditions
KW  - K-theory
KW  - linking coefficients
KW  - Dirac operators
KW  - spectral flow
KW  - elliptic operators
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25869
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Elliptic operators in even subspaces
N2  - An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.
T3  - Preprint - (1999) 10 
KW  - index of elliptic operators in subspaces
KW  - K-theory
KW  - eta invariant
KW  - Atiyah-Patodi-Singer theory
KW  - boundary value problems
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25461
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic operators in subspaces
N2  - We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.
T3  - Preprint - (2000) 04 
KW  - pseudodifferential subspaces
KW  - elliptic operators in subspaces
KW  - Fredholm property
KW  - index
KW  - K-theory
KW  - problem of classification
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25701
ER  -