The Radon transform on abelian groups
type: Item
instance of: scholarly article
title: The Radon transform on abelian groups
zbMATH Open document ID: 0607.43005
DOI: 10.1016/0097-3165(87)90071-9
author: Peter Frankl
author: Ron Graham
published in: Journal of Combinatorial Theory. Series A
publication date: 1987-01-01T00:00:00Z
review text: Let A be a finite group and let B be a subset of A. For any function \(f: A\to {\mathbb{C}}\), one can define the function \(F_ B: A\to {\mathbb{C}}\), called the Radon transform of f with respect to B by \(F_ B(a):=\sum_{b\in B}f(ab)\). The problem we address in this note is: for which subsets B is the Radon transform invertible ? Our main result gives a combinatorial description of such B in the case \(A={\mathbb{Z}}^ n_ 2\).
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 3981782
zbMATH Keywords: discrete Radon transform
zbMATH Keywords: invertible Radon transform
MaRDI profile type: Publication
full work available at URL: 0097-3165(87)90071-9
OpenAlex ID: W2099242518
cites work: The Radon transform on \({\mathbb{Z}}^ k_ 2\)
cites work: New light on Frobenius' creation of the theory of group characters
description: scientific article; zbMATH DE number 3981782