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Birkhäuser

The Localization Problem in Index Theory of Elliptic Operators

  • Book
  • © 2014

Overview

Authors:
  1. Vladimir Nazaikinskii

    1. Ishlinsky Inst. f. Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia

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  2. Bert-Wolfgang Schulze

    1. Universität Potsdam, Institut für Mathematik, Potsdam, Germany

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    You can also search for this author in PubMed   Google Scholar

  3. Boris Sternin

    1. Peoples’ Friendship Univers. of Russia, Moscow, Russia

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  • The book is concisely and clearly written and contains numerous figures helping the reader to visualize the material
  • The book uses simple language to explain the main ideas and avoids unnecessary technicalities without sacrificing mathematical rigor
  • The applications described in the book include a carefully selected variety of results, old as well as new, each of which is described in a self-contained way and can be read independently
  • Includes supplementary material: sn.pub/extras

Part of the book series: Pseudo-Differential Operators (PDO, volume 10)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
    Pages 1-17

  3. Superposition Principle

    1. Front Matter

      Pages 19-19
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    2. Superposition Principle for the Relative Index

      • Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
      Pages 21-40

    3. Superposition Principle for K-Homology

      • Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
      Pages 41-58

    4. Superposition Principle for KK-Theory

      • Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
      Pages 59-68

  4. Examples

    1. Front Matter

      Pages 69-69
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    2. Elliptic Operators on Noncompact Manifolds

      • Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
      Pages 71-79

    3. Applications to Boundary Value Problems

      • Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
      Pages 81-92

    4. Spectral Flow for Families of Dirac Type Operators with Classical Boundary Conditions

      • Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin
      Pages 93-108

  5. Back Matter

    Pages 109-117
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Keywords

About this book

The 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 new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.​

Authors and Affiliations

  • Ishlinsky Inst. f. Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia

    Vladimir Nazaikinskii

  • Universität Potsdam, Institut für Mathematik, Potsdam, Germany

    Bert-Wolfgang Schulze

  • Peoples’ Friendship Univers. of Russia, Moscow, Russia

    Boris Sternin

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