Abstract Coherent State Transforms Over Homogeneous Spaces of Compact Groups

2017 ◽  
Vol 12 (7) ◽  
pp. 1537-1548 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Coherent State ◽  
Homogeneous Spaces ◽  
Compact Groups

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

2018 ◽  
Vol 70 (1) ◽  
pp. 97-116 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Invariant Measure ◽  
Compact Group ◽  
Homogeneous Space ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Compact Groups ◽  
Compact Homogeneous Space ◽  
Linear Representations ◽  
Function Algebras ◽  
Convolution Function

AbstractThis paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. LetGbe a compact group andHa closed subgroup ofG. Letμbe the normalizedG-invariant measure over the compact homogeneous spaceG/Hassociated with Weil's formula and. We then present a structured class of abstract linear representations of the Banach convolution function algebrasLp(G/H,μ).

Abstract measure algebras over homogeneous spaces of compact groups

2018 ◽  
Vol 29 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Compact Group ◽  
Systematic Study ◽  
Measure Space ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Compact Groups ◽  
Coset Space ◽  
Left Coset ◽  
Abstract Measure

This paper presents a systematic study for abstract Banach measure algebras over homogeneous spaces of compact groups. Let [Formula: see text] be a closed subgroup of a compact group [Formula: see text] and [Formula: see text] be the left coset space associated to the subgroup [Formula: see text] in [Formula: see text]. Also, let [Formula: see text] be the Banach measure space consists of all complex measures over [Formula: see text]. Then we introduce the abstract notions of convolution and involution over the Banach measure space [Formula: see text].

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

2016 ◽  
Vol 101 (2) ◽  
pp. 171-187 ◽  
Author(s):  
ARASH GHAANI FARASHAHI
Keyword(s):  
Harmonic Analysis ◽  
Homogeneous Space ◽  
Semidirect Product ◽  
Homogeneous Spaces ◽  
Continuous Homomorphism ◽  
Compact Groups ◽  
Coset Space ◽  
Unified Approach ◽  
Left Coset ◽  
Semidirect Product Groups

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 $G_{\unicode[STIX]{x1D703}}/H$.

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