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Matrix Convolution Operators on Groups [electronic resource] /by Cho-Ho Chu.

by Chu, Cho-Ho [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 1956Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: IX, 114 p. online resource.ISBN: 9783540697985.Subject(s): Mathematics | Algebra | Harmonic analysis | Operator theory | Potential theory (Mathematics) | Global differential geometry | Mathematics | Operator Theory | Abstract Harmonic Analysis | Non-associative Rings and Algebras | Potential Theory | Differential GeometryDDC classification: 515.724 Online resources: Click here to access online
Contents:
Lebesgue Spaces of Matrix Functions -- Matrix Convolution Operators -- Convolution Semigroups.
In: Springer eBooksSummary: 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.
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Lebesgue Spaces of Matrix Functions -- Matrix Convolution Operators -- Convolution Semigroups.

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.

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