Multiparameter Eigenvalue Problems and Expansion Theorems

Download or read book Multiparameter Eigenvalue Problems and Expansion Theorems written by Hans Volkmer and published by Springer. This book was released on 2006-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.