1.

Record Nr.

UNINA9910483261703321

Autore

Chu Cho-Ho

Titolo

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

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2008

ISBN

3-540-69798-5

Edizione

[1st ed. 2008.]

Descrizione fisica

1 online resource (IX, 114 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434

Disciplina

512.2

Soggetti

Functions of complex variables

Differential geometry

Functional analysis

Operator theory

Harmonic analysis

Nonassociative rings

Rings (Algebra)

Functions of a Complex Variable

Differential Geometry

Functional Analysis

Operator Theory

Abstract Harmonic Analysis

Non-associative Rings and Algebras

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Lebesgue Spaces of Matrix Functions -- Matrix Convolution Operators -- Convolution Semigroups.

Sommario/riassunto

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.