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The Localization Problem in Index Theory of Elliptic Operators

  • Book
  • © 2014


  • 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:

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

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Table of contents (7 chapters)

  1. Superposition Principle

  2. Examples


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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