Algebraic Multiplicity of Eigenvalues of Linear Operators

  • J. López-Gómez
  • C. Mora-Corral
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

  • J. López-Gómez
    • 1
  • C. Mora-Corral
    • 2
  1. 1.Department of Applied MathematicsUniversidad Complutense de MadridMadridSpain
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-8401-2
  • Copyright Information Birkhäuser Verlag AG 2007
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8400-5
  • Online ISBN 978-3-7643-8401-2
  • About this book