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 focusis on the spectra and eigenspaces of convolution operators on these spaces, defined by matrix-valued measures. Among various spectral results, the L 2 -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 thisresult. 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. INDICE: 1. Introduction.- 2. Lebesgue spaces of matrix functions.- 3. Matrix convolution operators.- 4. Convolution semigroups.
- ISBN: 978-3-540-69797-8
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 130
- Fecha Publicación: 01/08/2008
- Nº Volúmenes: 1
- Idioma: Inglés