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Birkhäuser

Algebraic Multiplicity of Eigenvalues of Linear Operators

  • Book
  • © 2007

Overview

Authors:
  1. J. López-Gómez

    1. Department of Applied Mathematics, Universidad Complutense de Madrid, Madrid, Spain

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  2. C. Mora-Corral

    1. Mathematical Institute, University of Oxford, Oxford, UK

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  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Finite-dimensional Classic Spectral Theory

    1. Front Matter

      Pages 1-2
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    2. The Jordan Theorem

      Pages 3-35

    3. Operator Calculus

      Pages 37-62

    4. Spectral Projections

      Pages 63-73

  4. Nonlinear Spectral Theory

    1. Front Matter

      Pages 271-272
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    2. Nonlinear Eigenvalues

      Pages 273-293

  5. Back Matter

    Pages 295-310
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Keywords

About this book

This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operators with Fredholm index zero at a value of the parameter ? whereL(? ) is non-invertible. 0 0 Precisely, given K?{R,C}, two Banach spaces U and V over K, an open subset ? ? K,andapoint ? ? ?, our admissible operator families are the maps 0 r L?C (? ,L(U,V)) (1) for some r? N, such that L(? )? Fred (U,V); 0 0 hereL(U,V) stands for the space of linear continuous operatorsfrom U to V,and Fred (U,V) is its subset consisting of all Fredholm operators of index zero. From 0 the point of view of its novelty, the main achievements of this book are reached in case K = R, since in the case K = C and r = 1, most of its contents are classic, except for the axiomatization theorem of the multiplicity.

Authors and Affiliations

  • Department of Applied Mathematics, Universidad Complutense de Madrid, Madrid, Spain

    J. López-Gómez

  • Mathematical Institute, University of Oxford, Oxford, UK

    C. Mora-Corral

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