Abstract operator-valued Fourier transforms over homogeneous spaces of compact groups

2017 ◽  
Vol 11 (4) ◽  
pp. 1437-1467 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Fourier Transforms ◽  
Homogeneous Spaces ◽  
Compact Groups ◽  
Abstract Operator

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).

scholarly journals Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
David Maslan ◽  
Daniel N. Rockmore ◽  
Sarah Wolff
Keyword(s):  
Fourier Transform ◽  
Finite Groups ◽  
Fourier Transforms ◽  
Homogeneous Spaces ◽  
Separation Of Variables ◽  
Weyl Groups ◽  
General Linear Groups ◽  
International Audience ◽  
The Fourier Transform ◽  
A Finite Group

International audience We present a general diagrammatic approach to the construction of efficient algorithms for computingthe Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to theconstruction of Fast Fourier Transform algorithms we make explicit use of the path algebra connection and work inthe setting of quivers. In this setting the complexity of an algorithm for computing a Fourier transform reduces to pathcounting in the Bratelli diagram, and we generalize Stanley's work on differential posets to provide such counts. Ourmethods give improved upper bounds for computing the Fourier transform for the general linear groups over finitefields, the classical Weyl groups, and homogeneous spaces of finite groups.

scholarly journals Multipliers on spaces of functions on compact groups with p-summable Fourier transforms

1993 ◽  
Vol 47 (3) ◽  
pp. 435-442 ◽  
Author(s):  
Sanjiv Kumar Gupta ◽  
Shobha Madan ◽  
U.B. Tewari
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Fourier Transforms ◽  
Dual Group ◽  
Compact Groups ◽  
Circle Group ◽  
Integrable Functions ◽  
Space Of Integrable Functions

Let G be a compact abelian group with dual group Γ. For 1 ≤ p < ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.

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].

Sign in / Sign up

Export Citation Format

Share Document