The Localization Problem in Index Theory of Elliptic Operators, 1st Edition

  • Published By:
  • ISBN-10: 3034805101
  • ISBN-13: 9783034805100
  • DDC: 515.7242
  • Grade Level Range: College Freshman - College Senior
  • 117 Pages | eBook
  • Original Copyright 2014 | Published/Released May 2014
  • This publication's content originally published in print form: 2014

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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.​

Table of Contents

Front Cover.
Other Frontmatter.
Other Frontmatter.
Title Page.
Copyright Page.
1: Introduction.
2: Superposition Principle.
3: Superposition Principle for the Relative Index.
4: Superposition Principle for K.
5: Superposition Principle for KK-Theory.
6: Examples.
7: Elliptic Operators on Noncompact Manifolds.
8: Applications to Boundary Value Problems.
9: Spectral Flow for Families of Dirac Type Operators with Classical Boundary Conditions.