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.

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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
Industry Sectors: Energy, Utilities & Environment, Engineering, IT & Software

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Table of contents (7 chapters)

Front Matter

Introduction

Multiparameter eigenvalue problems for hermitian matrices

Multiparameter eigenvalue problems for bounded operators

Multiparameter eigenvalue problems for unbounded operators

Multiparameter expansion theorems for hermitian matrices

Multiparameter expansion theorems for bounded operators

Multiparameter expansion theorems for unbounded operators

Back Matter

About this book