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© 2007

Algebraic Multiplicity of Eigenvalues of Linear Operators

Benefits

  • Introduces readers to the classic theory with the most modern terminology, and, simultaneously, conducts readers comfortably to the latest developments in the theory of the algebraic multiplicity of eigenvalues of one-parameter families of Fredholm operators of index zero

  • Gives a very comfortable access to the latest developments in the real non-analytic case, where optimal results are included by the first time in a monograph

  • Recent results presented include the uniqueness of the algebraic multiplicity, which has important implications

Book
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Part of the Operator Theory: Advances and Applications book series (OT, volume 177)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Finite-dimensional Classic Spectral Theory

    1. Front Matter
      Pages 1-2
    2. Pages 3-35
    3. Pages 37-62
    4. Pages 63-73
  3. Algebraic Multiplicities

  4. Nonlinear Spectral Theory

    1. Front Matter
      Pages 271-272
    2. Pages 273-293
  5. Back Matter
    Pages 295-310

About this book

Introduction

This book brings together all the most important known results of research into the theory of algebraic multiplicities, from well-known classics like the Jordan Theorem to recent developments such as the uniqueness theorem and the construction of multiplicity for non-analytic families, which is presented in this monograph for the first time.

Part I (the first three chapters) is a classic course on finite-dimensional spectral theory; Part II (the next eight chapters) contains the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families; and Part III (the last chapter) transfers these results from linear to nonlinear analysis.

The text is as self-contained as possible. All the results are established in a finite-dimensional setting, if necessary. Furthermore, the structure and style of the book make it easy to access some of the most important and recent developments. Thus the material appeals to a broad audience, ranging from advanced undergraduates (in particular Part I) to graduates, postgraduates and reseachers who will enjoy the latest developments in the real non-analytic case (Part II).

Keywords

Eigenvalue Matrix Matrix Theory algebraic multiplicity spectral theory

Authors and affiliations

  1. 1.Department of Applied MathematicsUniversidad Complutense de MadridMadridSpain
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK

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