Matrix Convolution Operators on Groups

Chu, Cho-Ho

ISBN 10: 3540697977 ISBN 13: 9783540697978

Verlag: Springer, 2008

Sprache: Englisch

Zustand: Neu Softcover

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Bibliografische Details

Titel

Matrix Convolution Operators on Groups

Verlag

Springer

Erscheinungsjahr

2008

Sprache

Englisch

ISBN-10

3540697977

ISBN-13

9783540697978

Einband

Softcover

Zustand

New

Verk�uferkataloge

�ber diesen Titel

Inhaltsangabe

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 Lp 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.

Von der hinteren Coverseite

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^pspaces 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.

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