Multiparameter Eigenvalue Problems and Expansion Theorems

Hans Volkmer (auth.)3540504796, 9783540504795, 0387504796

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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Table of contents :
Introduction….Pages 1-7
Multiparameter eigenvalue problems for hermitian matrices….Pages 8-20
Multiparameter eigenvalue problems for bounded operators….Pages 21-49
Multiparameter eigenvalue problems for unbounded operators….Pages 50-75
Multiparameter expansion theorems for hermitian matrices….Pages 76-86
Multiparameter expansion theorems for bounded operators….Pages 87-115
Multiparameter expansion theorems for unbounded operators….Pages 116-141