The Radon transform on \({\mathbb{Z}}^ k_ 2\)
type: Item
instance of: scholarly article
title: The Radon transform on \({\mathbb{Z}}^ k_ 2\)
zbMATH Open document ID: 0581.43001
author: Persi Diaconis
author: Ron Graham
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The paper investigates the uniqueness of the discrete Radon transform in various particular cases. For example, if \(S_ n\) is the symmetric group on n letters, \(Y=\{\pi \in S_ n:\) \(d(id,\pi)\leq 1\}\) where d is the Cayley metric, it is proved that the Radon transform of a function \(f: S_ n\to {\mathbb{R}}\), given by \(f_ Y(x)=\sum_{y\in Y+x}f(y)\) is one to one if and only if \(n\in \{1,3,4,5,6,8,10,12\}\).
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 20D99
Mathematics Subject Classification ID: 20B30
Mathematics Subject Classification ID: 44A55
zbMATH DE Number: 3929650
zbMATH Keywords: discrete Radon transform
zbMATH Keywords: symmetric group
MaRDI profile type: Publication
full work available at URL: pjm.1985.118.323
OpenAlex ID: W1551972025
DOI: 10.2140/PJM.1985.118.323
description: scientific article; zbMATH DE number 3929650