04094nam 22008295 450 991048326170332120200630025905.03-540-69798-510.1007/978-3-540-69798-5(CKB)1000000000437222(SSID)ssj0000318855(PQKBManifestationID)11265704(PQKBTitleCode)TC0000318855(PQKBWorkID)10337213(PQKB)10858637(DE-He213)978-3-540-69798-5(MiAaPQ)EBC3063140(MiAaPQ)EBC6281345(PPN)128124709(EXLCZ)99100000000043722220100301d2008 u| 0engurnn|008mamaatxtccrMatrix Convolution Operators on Groups[electronic resource] /by Cho-Ho Chu1st ed. 2008.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2008.1 online resource (IX, 114 p.) Lecture Notes in Mathematics,0075-8434Bibliographic Level Mode of Issuance: Monograph3-540-69797-7 Includes bibliographical references and index.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.Lecture Notes in Mathematics,0075-8434Functions of complex variablesDifferential geometryFunctional analysisOperator theoryHarmonic analysisNonassociative ringsRings (Algebra)Functions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Abstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Non-associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11116Functions 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.512.2Chu Cho-Hoauthttp://id.loc.gov/vocabulary/relators/aut66924MiAaPQMiAaPQMiAaPQBOOK9910483261703321Matrix Convolution Operators on Groups230595UNINA