TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Matrix Convolution Operators on Groups
T2  - Lecture Notes in Mathematics,
SN  - 9783540697985
AV  - QA329-329.9 
U1  - 515.724 23
PY  - 2008///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Algebra
KW  - Harmonic analysis
KW  - Operator theory
KW  - Potential theory (Mathematics)
KW  - Global differential geometry
KW  - Operator Theory
KW  - Abstract Harmonic Analysis
KW  - Non-associative Rings and Algebras
KW  - Potential Theory
KW  - Differential Geometry
N1  - Lebesgue Spaces of Matrix Functions -- Matrix Convolution Operators -- Convolution Semigroups; ZDB-2-SMA; ZDB-2-LNM
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-540-69798-5
ER  -