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ABSTRACT HARMONIC ANALYSIS OF RELATIVE CONVOLUTIONS OVER CANONICAL HOMOGENEOUS SPACES OF SEMIDIRECT PRODUCT GROUPS

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  16 March 2016

ARASH GHAANI FARASHAHI
ARASH GHAANI FARASHAHI*
Affiliation:
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna, Vienna, Austria email arash.ghaani.farashahi@univie.ac.at, ghaanifarashahi@hotmail.com
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Abstract

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This paper presents a structured study for abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups. Let $H,K$ be locally compact groups and $\unicode[STIX]{x1D703}:H\rightarrow \text{Aut}(K)$ be a continuous homomorphism. Let $G_{\unicode[STIX]{x1D703}}=H\ltimes _{\unicode[STIX]{x1D703}}K$ be the semidirect product of $H$ and $K$ with respect to $\unicode[STIX]{x1D703}$ and $G_{\unicode[STIX]{x1D703}}/H$ be the canonical homogeneous space (left coset space) of $G_{\unicode[STIX]{x1D703}}/H$. We present a unified approach to the harmonic analysis of relative convolutions over the canonical homogeneous space $G_{\unicode[STIX]{x1D703}}/H$.

Keywords

canonical homogeneous space of semidirect groupsrho-function𝜃-convolution𝜃-involutionrelative convolutions

MSC classification

Primary: 43A85: Analysis on homogeneous spaces
Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 101 , Issue 2 , October 2016 , pp. 171 - 187
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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