Matrix Convolution Operators on Groups

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.

List of contents

Lebesgue Spaces of Matrix Functions.- Matrix Convolution Operators.- Convolution Semigroups.

Summary

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.

Product details

• Authors: Cho-Ho Chu
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 23.02.2011
• EAN: 9783540697978
• ISBN: 978-3-540-69797-8
• No. of pages: 114
• Dimensions: 155 mm x 7 mm x 235 mm
• Weight: 222 g
• Illustrations: IX, 114 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Algebra, B, Funktionalanalysis und Abwandlungen, Mathematics and Statistics, Functional Analysis, Differential Geometry, Rings (Algebra), Non-associative Rings and Algebras, Nonassociative rings, Complex analysis, complex variables, Abstract Harmonic Analysis, Harmonic analysis, Functional analysis & transforms, Operator Theory, Functions of a Complex Variable, Functions of complex variables, Differential & Riemannian geometry