rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: Localization Problem in Index Theory of Elliptic Operators
  name:
    name part: Nazaikinskii, Vladimir.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Schulze, Bert-Wolfgang.
    role:
      role term: author.
  name:
    name part: Sternin, Boris.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 117 p. 38 illus., 1 illus. in color. online resource.
  abstract: This book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of important new problems in index theory. So far, the localization principle has scarcely been covered in journal papers. The present book is intended to fill this gap. Both the general localization principle and its applications to specific problems, old and new, are covered. Concisely and clearly written, this monograph includes numerous figures helping the reader to visualize the material. The Localization Problem in Index Theory of Elliptic Operators will be of interest to researchers as well as graduate and postgraduate students specializing in differential equations and related topics.
  table of contents: Preface -- Introduction -- 0.1 Basics of Elliptic Theory -- 0.2 Surgery and the Superposition Principle -- 0.3 Examples and Applications -- 0.4 Bibliographical Remarks -- Part I: Superposition Principle -- 1 Superposition Principle for the Relative Index -- 1.1 Collar Spaces -- 1.2 Proper Operators and Fredholm Operators -- 1.3 Superposition Principle -- 2 Superposition Principle for K-Homology -- 2.1 Preliminaries -- 2.2 Fredholm Modules and K-Homology -- 2.3 Superposition Principle -- 2.4 Fredholm Modules and Elliptic Operators -- 3 Superposition Principle for KK-Theory -- 3.1 Preliminaries -- 3.2 Hilbert Modules, Kasparov Modules, and KK -- 3.3 Superposition Principle -- Part II: Examples -- 4 Elliptic Operators on Noncompact Manifolds -- 4.1 Gromov–Lawson Theorem -- 4.2 Bunke Theorem -- 4.3 Roe’s Relative Index Construction -- 5 Applications to Boundary Value Problems -- 5.1 Preliminaries -- 5.2 Agranovich–Dynin Theorem -- 5.3 Agranovich Theorem -- 5.4 Bojarski Theorem and Its Generalizations -- 5.5 Boundary Value Problems with Symmetric Conormal Symbol -- 6 Spectral Flow for Families of Dirac Type Operators -- 6.1 Statement of the Problem -- 6.2 Simple Example -- 6.3 Formula for the Spectral Flow -- 6.4 Computation of the Spectral Flow for a Graphene Sheet -- Bibliography.
  note: by Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin.
  subject:
    topic: Mathematics
  subject:
    topic: K-theory
  subject:
    topic: Functional analysis
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematics
  subject:
    topic: Global Analysis and Analysis on Manifolds
  subject:
    topic: K-Theory
  subject:
    topic: Functional Analysis
  subject:
    topic: Partial Differential Equations
  classification: QA614-614.97
  classification: 514.74
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Pseudo-Differential Operators, Theory and Applications ; 10
  identifier: 9783034805100
  identifier: http://dx.doi.org/10.1007/978-3-0348-0510-0
  record info:
    record creation date: 131125
    record change date: 20151204150239.0
    record identifier: 978-3-0348-0510-0