Abstract Poisson summation formulas over homogeneous spaces of compact groups
type: Item
instance of: scholarly article
title: Abstract Poisson summation formulas over homogeneous spaces of compact groups
zbMATH Open document ID: 1409.43004
author: Arash Ghaani Farashahi
published in: Analysis and Mathematical Physics
publication date: 2017-12-01T00:00:00Z
review text: Let \(G\) be a compact group and \(H\) be a closed subgroup of \(G\). The author studies some abstract aspects of harmonic analysis on Banach function spaces over the compact homogeneous space \(G/H\). He introduces the abstract notion of dual space \(\widehat{G/H}\) for the homogeneous space \(G/H\) and presents the theoretical definition of the abstract operator-valued Fourier transform over the compact homogeneous space \(G/H\). He also proves that the abstract Fourier transform over \(G/H\) satisfies a generalized version of the Poisson summation formula.
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 43A90
zbMATH DE Number: 6814658
zbMATH Keywords: compact group
zbMATH Keywords: homogeneous space
zbMATH Keywords: dual homogeneous space
zbMATH Keywords: Fourier transform
zbMATH Keywords: Plancherel (trace) formula
zbMATH Keywords: inversion formula
zbMATH Keywords: Poisson summation formula
Wikidata QID: Q59607556
reviewed by: M. J. Mehdipour
MaRDI profile type: Publication
full work available at URL: s13324-016-0156-2
OpenAlex ID: W2552919413
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DOI: 10.1007/S13324-016-0156-2
description: scientific article; zbMATH DE number 6814658