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ABSTRACT HARMONIC ANALYSIS OF RELATIVE CONVOLUTIONS OVER CANONICAL HOMOGENEOUS SPACES OF SEMIDIRECT PRODUCT GROUPS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 101 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 16 March 2016, pp. 171-187
- Print publication:
- October 2016
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- Article
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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 
$G_{\unicode[STIX]{x1D703}}/H$.
