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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978-3-540-46015-2 (9783540460152)
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Schweitzer Klassifikation
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.
