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Multiparameter Eigenvalue Problems and Expansion Theorems

  • Book
  • © 1988

Overview

Authors:
  1. Hans Volkmer
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1356)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Hans Volkmer
    Pages 1-7

  3. Multiparameter eigenvalue problems for hermitian matrices

    • Hans Volkmer
    Pages 8-20

  4. Multiparameter eigenvalue problems for bounded operators

    • Hans Volkmer
    Pages 21-49

  5. Multiparameter eigenvalue problems for unbounded operators

    • Hans Volkmer
    Pages 50-75

  6. Multiparameter expansion theorems for hermitian matrices

    • Hans Volkmer
    Pages 76-86

  7. Multiparameter expansion theorems for bounded operators

    • Hans Volkmer
    Pages 87-115

  8. Multiparameter expansion theorems for unbounded operators

    • Hans Volkmer
    Pages 116-141

  9. Back Matter

    Pages 142-157
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Keywords

About this book

This book provides a self-contained treatment of two of the main problems of multiparameter spectral theory: the existence of eigenvalues and the expansion in series of eigenfunctions. The results are first obtained in abstract Hilbert spaces and then applied to integral operators and differential operators. Special attention is paid to various definiteness conditions which can be imposed on multiparameter eigenvalue problems. The reader is not assumed to be familiar with multiparameter spectral theory but should have some knowledge of functional analysis, in particular of Brower's degree of maps.

Bibliographic Information

  • Book Title: Multiparameter Eigenvalue Problems and Expansion Theorems

  • Authors: Hans Volkmer

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0089295

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-50479-5Published: 07 December 1988

  • eBook ISBN: 978-3-540-46015-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 162

  • Topics: Analysis

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