Matrix Convolution Operators on Groups

Cho-Ho Chu

ISBN 10: 3540697977 / ISBN 13: 9783540697978

Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 2008, 2008

Beschreibung

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 128 pp. Englisch.

Bestandsnummer des Verkäufers 9783540697978

Bibliografische Details

• Titel: Matrix Convolution Operators on Groups
• Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 2008
• Erscheinungsjahr: 2008
• Sprache: Englisch
• ISBN-10: 3540697977
• ISBN-13: 9783540697978
• Einband: Taschenbuch
• Zustand: Neu

Über 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.