Titlebook: Matrix Convolution Operators on Groups; Cho-Ho Chu Book 2008 Springer-Verlag Berlin Heidelberg 2008 Harmonic function.Jordan algebra.Matri

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978-3-540-69797-8Springer-Verlag Berlin Heidelberg 2008

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Lebesgue Spaces of Matrix Functions,velopments. We recall some basic definitions and derive some results for convolution operators in the scalar case. We discuss differentiability of the norm in ..(.,.. which is needed later, and compute the Gateaux derivative of the norm when the matrix space .. is equipped with the Hilbert-Schmidt norm.

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Matrix Convolution Operators,tiplication necessitates the introduction of the . convolution operator L. : . ?σ *? . for a consistent duality theory. We first characterise these operators and show they are translation invariant operators satisfying some continuity condition.We also determine when these operators are weakly compact on L. and L. spaces.

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https://doi.org/10.1007/978-3-540-69798-5Harmonic function; Jordan algebra; Matrix; Matrix convolution operator; Riemannian symmetric space; Spect

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0075-8434 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 focus is on the spectra and eigenspaces of convolution operators on these spaces, defined by matrix

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Book 2008nts 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 focus is on the spectra and eigenspaces of convolution operators on these spaces, defined by matrix-valued measures. Among various spectral re

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Book 2008ph 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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Introduction,escribed in depth in [6], and the Fredholm properties of finite sums of weighted shift operators on ?.spaces of Banach space valued functions on ?. have been analysed in detail in [54]. Convolution operators on ..spaces of real and complex functions are well-studied in literature, however, there are