Fourier transform imitations
type: Item
instance of: scholarly article
title: Fourier transform imitations
zbMATH Open document ID: 0873.43004
DOI: 10.1016/S0024-3795(96)00153-X
author: Ron Aharoni
author: Milton Maritz
author: Roy Meshulam
published in: Linear Algebra and its Applications
publication date: 1997-10-29T00:00:00Z
review text: Let \(G\) be a finite Abelian group, and \(L(G)\) the space of all complex-valued functions on \(G\). Let \(m\) be the maximal order of an element of \(G\), and \(C_m\) the group of \(m\)th roots of unity. For any \(u\in L(C_m)\) we define \(S_u:L(\widehat G)\to L(G)\) by \(S_uf(\chi)= \sum_{x\in G} u(\chi(-x))f(\chi)\). Observe that, for \(u\equiv 1\), \(S_u\) is the Fourier transform on \(\widehat G\). The paper establishes necessary and sufficient conditions for \(S_u\) to be invertible.
reviewed by: John W.Baker
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 1011325
zbMATH Keywords: finite Abelian group
zbMATH Keywords: complex-valued functions
zbMATH Keywords: Fourier transform
MaRDI profile type: Publication
cites work: Q3943153
cites work: Q4126536
cites work: Q3480228
description: scientific article; zbMATH DE number 1011325