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# A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups

Published:2017-02-21
Printed: Feb 2018
• Arash Ghaani Farashahi,
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna
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## Abstract

This paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ be a closed subgroup of $G$. Let $\mu$ be the normalized $G$-invariant measure over the compact homogeneous space $G/H$ associated to the Weil's formula and $1\le p\lt \infty$. We then present a structured class of abstract linear representations of the Banach convolution function algebras $L^p(G/H,\mu)$.
 Keywords: homogeneous space, linear representation, continuous unitary representation, convolution function algebra, compact group, convolution, involution
 MSC Classifications: 43A85 - Analysis on homogeneous spaces 47A67 - Representation theory 20G05 - Representation theory

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