Matrix Convolution Operators on Groups

  • Cho-Ho Chu

Part of the Lecture Notes in Mathematics book series (LNM, volume 1956)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pages 1-4
  3. Pages 87-100
  4. Back Matter
    Pages 101-108

About this book

Introduction

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.

Keywords

Harmonic function Jordan algebra Matrix Matrix convolution operator Riemannian symmetric space Spectral theory algebra convolution

Authors and affiliations

  • Cho-Ho Chu
    • 1
  1. 1.School of Mathematical Sciences Queen MaryUniversity of LondonLondonUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-69798-5
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-69797-8
  • Online ISBN 978-3-540-69798-5
  • Series Print ISSN 0075-8434
  • About this book