Lecture Notes in Mathematics

Chu, Cho-Ho

In the last decade, convolution operators of matrix functions have received unusual attention due to their diverse applications. This monograph presents some new developments in the spectral theory of these operators. The setting is the L^p spaces of matrix-valued functions on locally compact groups. The focus is on the spectra and eigenspaces of convolution operators on these spaces, defined by matrix-valued measures. Among various spectral results, the L²-spectrum of such an operator is completely determined and as an application, the spectrum of a discrete Laplacian on a homogeneous graph is computed using this result. The contractivity properties of matrix convolution semigroups are studied and applications to harmonic functions on Lie groups and Riemannian symmetric spaces are discussed. An interesting feature is the presence of Jordan algebraic structures in matrix-harmonic functions.

Details

Published by: Springer

Publication Date: 2008-08-25

Format: Paperback

ISBN-13: 9783540697978

DOI: 10.1007/978-3-540-69798-5

Dimensions: 235cm x155cm

Pages: 114