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This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on L^p spaces, arriving at a description of these operators and L^p versions of the theorems of Wiener and Kaplansky-Helson.
List of contents
1 Elementary Results.- 2 An Approximation Theorem for CV2(G).- 3 The Figa-Talamanca Herz Algebra.- 4 The Dual of Ap(G).- 5 CVp(G) as a Module on Ap(G).- 6 The Support of a Convolution Operator.- 7 Convolution Operators Supported by Subgroups.- 8 CVp(G) as a Subspace of CV2(G).
Summary
This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson.
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From the reviews:
“This is a useful, self-contained introduction to the Banach algebra of convolution operators on a locally compact group G … . It is the first book dedicated to this topic, gathering results mainly due to Herz and, among others, to Lohoué and the author of the book. Many references on related topics are given in the notes.” (Françoise Lust-Piquard, Mathematical Reviews, Issue 2012 e)
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From the reviews:
"This is a useful, self-contained introduction to the Banach algebra of convolution operators on a locally compact group G ... . It is the first book dedicated to this topic, gathering results mainly due to Herz and, among others, to Lohoué and the author of the book. Many references on related topics are given in the notes." (Françoise Lust-Piquard, Mathematical Reviews, Issue 2012 e)
