@article{SavinSternin2005,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Boundary value problems on manifolds with fibered boundary},
  issn      = {0025-584X},
  year      = {2005},
  abstract  = {We define a class of boundary value problems on manifolds with fibered boundary. This class is in a certain sense a deformation between the classical boundary value problems and the Atiyah-Patodi-Singer problems in subspaces (it contains both as special cases). The boundary conditions in this theory are taken as elements of the C*-algebra generated by pseudodifferential operators and families of pseudodifferential operators in the fibers. We prove the Fredholm. property for elliptic boundary value problems and compute a topological obstruction (similar to Atiyah-Bott obstruction) to the existence of elliptic boundary conditions for a given elliptic operator. Geometric operators with trivial and nontrivial obstruction are given. (c) 2005 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
  language  = {en}
}
@book{SavinSternin2005,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Pseudodifferential subspaces and their applications in elliptic theory},
  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     = {46 S.},
  year      = {2005},
  language  = {en}
}
@book{NazajkinskijSternin2002,
  author    = {Nazajkinskij, Vladimir E. and Sternin, Boris},
  title     = {Relative elliptic theory},
  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     = {74 S.},
  year      = {2002},
  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@unpublished{SavinSternin2000,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{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{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}
}
@unpublished{NazaikinskiiSternin2002,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {Relative elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26400},
  year      = {2002},
  abstract  = {This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms.},
  language  = {en}
}
@unpublished{NazaikinskiiSternin2001,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {Some problems of control of semiclassical states for the Schr{\"o}dinger equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26130},
  year      = {2001},
  abstract  = {Contents: Introduction Controlled Quantum Systems The Asymptotic Controllability Problem The Stabilization Problem Unitarily Nonlinear Equations The Quantum Problem The Stabilization Problem for the Schr{\"o}dinger Equation with a Unitarily Non-linear Control},
  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}
}
@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}
}
@book{NazajkinskijSternin2001,
  author    = {Nazajkinskij, Vladimir E. and Sternin, Boris},
  title     = {Some problems of control of semiclassical states for the schr{\"o}dinger equation},
  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     = {30 S.},
  year      = {2001},
  language  = {en}
}
@book{SavinSternin2001,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Index defects in the theorie of nonlocal boundary value problems and the n-invariant},
  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     = {53 S.},
  year      = {2001},
  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{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{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{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}
}