@unpublished{SchulzeSterninShatalov1997,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@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Operator algebras on singular manifolds. IV, V},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25062},
  year      = {1997},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On general boundary value problems for elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25138},
  year      = {1997},
  abstract  = {We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Nonstationary problems for equations of Borel-Fuchs type},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24973},
  year      = {1997},
  abstract  = {In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out.},
  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@unpublished{SchulzeSterninShatalov1997,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}
}
@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{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}
}
@unpublished{SchulzeNazaikinskiiSterninetal.1997,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris and Shatalov, Victor},
  title     = {Spectral boundary value problems and elliptic equations on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25147},
  year      = {1997},
  abstract  = {For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.},
  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{SchulzeNazaikinskiiSternin1998,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25296},
  year      = {1998},
  abstract  = {For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space.},
  language  = {en}
}
@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}
}
@unpublished{SavinSternin2000,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Eta-invariant and Pontrjagin duality in K-theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25747},
  year      = {2000},
  abstract  = {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.},
  language  = {en}
}
@unpublished{SavinSternin2005,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Pseudodifferential subspaces and their applications in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29937},
  year      = {2005},
  abstract  = {The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah-Patodi-Singer eta invariant, when it defines a homotopy invariant (Gilkey's problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.},
  language  = {en}
}
@unpublished{SavinSternin1999,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Elliptic operators in odd subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25478},
  year      = {1999},
  abstract  = {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.},
  language  = {en}
}
@unpublished{SavinSternin2001,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Index defects in the theory of nonlocal boundary value problems and the η-invariant},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26146},
  year      = {2001},
  abstract  = {The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincar{\´e} duality in the K-theory of the corresponding manifolds with singularities.},
  language  = {en}
}
@unpublished{SavinSternin2000,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Eta invariant and parity conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25869},
  year      = {2000},
  abstract  = {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.},
  language  = {en}
}
@unpublished{SavinSternin1999,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Elliptic operators in even subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25461},
  year      = {1999},
  abstract  = {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.},
  language  = {en}
}
@unpublished{SavinSchulzeSternin1998,
  author    = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {On the invariant index formulas for spectral boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25285},
  year      = {1998},
  abstract  = {In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms.},
  language  = {en}
}
@unpublished{SavinSchulzeSternin2000,
  author    = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic operators in subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25701},
  year      = {2000},
  abstract  = {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.},
  language  = {en}
}
@unpublished{NazaikinskiiSternin2000,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {On surgery in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25873},
  year      = {2000},
  abstract  = {We prove a general theorem on the behavior of the relative index under surgery 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.},
  language  = {en}
}