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A Class of Abstract Linear Representations for Convolution Function Algebras overHomogeneous Spaces of Compact Groups

Published online by Cambridge University Press:  20 November 2018

Arash Ghaani Farashahi
Arash Ghaani Farashahi*
Affiliation:
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna e-mail: arash.ghaani.farashahi@univie.ac.atghaanifarashahi@hotmail.com
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Abstract

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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 $H$ a closed subgroup of $G$. Let $\mu $ be the normalized $G$-invariant measure over the compact homogeneous space $G/H$ associated with Weil's formula and $1\,\le \,p\,<\,\infty $. We then present a structured class of abstract linear representations of the Banach convolution function algebras ${{L}^{p}}\left( G/H,\,\mu \right)$.

Keywords

43A8547A6720G05homogeneous spacelinear representationcontinuous unitary representationconvolution function algebracompact groupconvolutioninvolution
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 1 , 01 February 2018 , pp. 97 - 116
Copyright
Copyright © Canadian Mathematical Society 2018

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