@unpublished{SavinSternin2005,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@unpublished{NazaikinskiiSavinSchulzeetal.2004,
  author    = {Nazaikinskii, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {On the homotopy classification of elliptic operators on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26769},
  year      = {2004},
  abstract  = {We obtain a stable homotopy classification of elliptic operators on manifolds with edges.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2004,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 6: Elliptic theory on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26757},
  year      = {2004},
  abstract  = {Contents: Chapter 6: Elliptic Theory on Manifolds with Edges Introduction 6.1. Motivation and Main Constructions 6.1.1. Manifolds with edges 6.1.2. Edge-degenerate differential operators 6.1.3. Symbols 6.1.4. Elliptic problems 6.2. Pseudodifferential Operators 6.2.1. Edge symbols 6.2.2. Pseudodifferential operators 6.2.3. Quantization 6.3. Elliptic Morphisms and the Finiteness Theorem 6.3.1. Matrix Green operators 6.3.2. General morphisms 6.3.3. Ellipticity, Fredholm property, and smoothness Appendix A. Fiber Bundles and Direct Integrals A.1. Local theory A.2. Globalization A.3. Versions of the Definition of the Norm},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2004,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26700},
  year      = {2004},
  abstract  = {Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. 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 5: Manifolds with isolated singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26659},
  year      = {2003},
  abstract  = {Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Ellipticity and the finiteness theorem 5.4. Calculus of ΨDO 5.4.1. General ΨDO 5.4.2. The subalgebra of stabilizing ΨDO 5.4.3. Ellipticity and the finiteness theorem},
  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}
}
@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 1: Localization (surgery) in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26546},
  year      = {2003},
  abstract  = {Contents: Chapter 1: Localization (Surgery) in Elliptic Theory 1.1. The Index Locality Principle 1.1.1. What is locality? 1.1.2. A pilot example 1.1.3. Collar spaces 1.1.4. Elliptic operators 1.1.5. Surgery and the relative index theorem 1.2. Surgery in Index Theory on Smooth Manifolds 1.2.1. The Booß-Wojciechowski theorem 1.2.2. The Gromov-Lawson theorem 1.3. Surgery for Boundary Value Problems 1.3.1. Notation 1.3.2. General boundary value problems 1.3.3. A model boundary value problem on a cylinder 1.3.4. The Agranovich-Dynin theorem 1.3.5. The Agranovich theorem 1.3.6. Bojarski's theorem and its generalizations 1.4. (Micro)localization in Lefschetz theory 1.4.1. The Lefschetz number 1.4.2. Localization and the contributions of singular points 1.4.3. The semiclassical method and microlocalization 1.4.4. The classical Atiyah-Bott-Lefschetz theorem},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2003,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : V. Index formulas for elliptic problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26500},
  year      = {2003},
  abstract  = {For elliptic problems on manifolds with edges, we construct index formulas in form of a sum of homotopy invariant contributions of the strata (the interior of the manifold and the edge). Both terms are the indices of elliptic operators, one of which acts in spaces of sections of finite-dimensional vector bundles on a compact closed manifold and the other in spaces of sections of infinite-dimensional vector bundles over the edge.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26415},
  year      = {2002},
  abstract  = {The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.},
  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{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26386},
  year      = {2002},
  abstract  = {When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26335},
  year      = {2002},
  abstract  = {Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26327},
  year      = {2002},
  abstract  = {We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.},
  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{NazaikinskiiSchulzeSternin2001,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Localization problem in index theory of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26175},
  year      = {2001},
  abstract  = {This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.},
  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{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{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{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{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 11: Noncommutative analysis and high-frequency asymptotics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25857},
  year      = {2000},
  abstract  = {Content: Chapter 11: Noncommutative Analysis and High-Frequency Asymptotics 11.1 Statement of the Problem 11.2 Mixed Asymptotics: the General Scheme 11.3 The Asymptotic Solution of Main Problem 11.4 Analysis of the Asymptotic Solution},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 3: Applications of noncommutative analysis to operator algebras on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25801},
  year      = {2000},
  abstract  = {Content: Chapter 3: Applications of Noncommutative Analysis to Operator Algebras on Singular Manifolds 3.1 Statement of the problem 3.2 Operators on the Model Cone 3.3 Operators on the Model Cusp of Order k 3.4 An Application to the Construction of Regularizers and Proof of the Finiteness Theorem},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 2: Exactly soluble commutation relations (The simplest class of classical mechanics)},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25796},
  year      = {2000},
  abstract  = {Content: Chapter 2: Exactly SolubleCommutation Relations (The Simplest Class of Classical Mechanics) 2.1 Some examples 2.2 Lie commutation relations 2.3 Non-Lie (nonlinear) commutation relations},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Part II: Quantization by the method of ordered operators (Noncommutative Analysis) : Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25762},
  year      = {2000},
  abstract  = {Content: 0.1 Preliminary Remarks Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems 1.1 Functions of One Operator (Functional Calculi) 1.2 Functions of Several Operators 1.3 Main Formulas of Operator Calculus 1.4 Main Tools of Noncommutative Analysis 1.5 Composition Laws and Ordered Representations},
  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{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{NazaikinskiiSchulzeSternin1999,
  author    = {Nazaikinskii, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25582},
  year      = {1999},
  abstract  = {In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.},
  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{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}
}
@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{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{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{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{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{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{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{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{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{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Quantization of symplectic transformations on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25084},
  year      = {1997},
  abstract  = {The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {A Lefschetz fixed point theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25073},
  year      = {1997},
  abstract  = {We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points.},
  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     = {Operator algebras on singular manifolds. I},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25011},
  year      = {1997},
  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     = {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}
}