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Über dieses Buch

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.​

Inhaltsverzeichnis

Frontmatter

2014 | OriginalPaper | Buchkapitel

Chapter 0. Introduction

Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin

Superposition Principle

Frontmatter

2014 | OriginalPaper | Buchkapitel

Chapter 1. Superposition Principle for the Relative Index

Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin

2014 | OriginalPaper | Buchkapitel

Chapter 2. Superposition Principle for K-Homology

Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin

2014 | OriginalPaper | Buchkapitel

Chapter 3. Superposition Principle for KK-Theory

Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin

Examples

Frontmatter

2014 | OriginalPaper | Buchkapitel

Chapter 4. Elliptic Operators on Noncompact Manifolds

Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin

2014 | OriginalPaper | Buchkapitel

Chapter 5. Applications to Boundary Value Problems

Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin

2014 | OriginalPaper | Buchkapitel

Chapter 6. Spectral Flow for Families of Dirac Type Operators with Classical Boundary Conditions

Vladimir Nazaikinskii, Bert-Wolfgang Schulze, Boris Sternin

Backmatter

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