Fourier analysis of subgroup conjugacy invariant functions on finite groups
type: Item
instance of: scholarly article
title: Fourier analysis of subgroup conjugacy invariant functions on finite groups
zbMATH Open document ID: 1271.43006
author: Fabio Scarabotti
author: Filippo Tolli
published in: Monatshefte für Mathematik
publication date: 2013-06-17T00:00:00Z
review text: The article deals with a variant of the Fourier transform on the convolution algebra \(\mathcal{C}(G,H)\) of complex-valued functions on a finite group \(G\), invariant under the conjugation action of its subgroup \(H\). An orthogonal basis of \(\mathcal{C}(G,H)\) is found and used to establish an algebra isomorphism -- a ``Fourier transform'' -- between \(\mathcal{C}(G,H)\) and a certain direct sum of matrix algebras. It is accompanied by a corresponding inversion formula and Plancherel's formula. The theory is then specialized to the center of \(\mathcal{C}(G,H)\), yielding a spherical Fourier transform. The authors also provide an example involving the symmetric group, and propose, under some additional assumptions, a canonical choice of the basis of \(\mathcal{C}(G,H)\).
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 6176424
zbMATH Keywords: conjugacy invariant functions
zbMATH Keywords: finite Fourier transform
zbMATH Keywords: Gelfand pair
MaRDI profile type: Publication
full work available at URL: s00605-012-0445-2
OpenAlex ID: W1966934241
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DOI: 10.1007/S00605-012-0445-2
description: scientific article; zbMATH DE number 6176424