Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Matrix Convolution Operators on Groups
Authors: Cho-Ho Chu
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-69798-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Softcover ISBN: 978-3-540-69797-8Published: 25 August 2008
eBook ISBN: 978-3-540-69798-5Published: 15 August 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 114
Topics: Functions of a Complex Variable, Differential Geometry, Functional Analysis, Operator Theory, Abstract Harmonic Analysis, Non-associative Rings and Algebras