Diophantine integral geometry
type: Item
instance of: scholarly article
title: Diophantine integral geometry
zbMATH Open document ID: 1182.44002
author: A. Abouelaz
author: Abdallah Ihsane
published in: Mediterranean Journal of Mathematics
publication date: 2008-06-25T00:00:00Z
review text: The Radon transform of \(f\) is defined as the function \(R_{c}f:\mathbb{P}_{n}\to \mathbb{C}\) given by \[ R_{c}f(t,\omega)=\int_{H(t,\omega)}f(x)\,d\mu(x), \quad \text{for all}\quad (t,\omega)\in \mathbb{R}\times S^{n-1}, \] where \(d\mu\) is the Euclidean measure on the hyperplane \(H(t,\omega)\). The authors investigate the Radon transform \(R\) on discrete hyperplanes in the lattice \(\mathbb{Z}^{n}\) \((n\geq 2)\) defined by linear diophantine equations. More precisely, they study specific properties of the discrete Radon transform \(R\) and its dual \(R^{\ast}\), an inversion formula for \(R\) and an appropriate support theorem in the discrete case.
reviewed by: Osman Yürekli
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 11D04
Mathematics Subject Classification ID: 65T50
zbMATH DE Number: 5292749
zbMATH Keywords: linear diophantine equations
zbMATH Keywords: discrete Radon transform
zbMATH Keywords: inversion formula
zbMATH Keywords: support theorem
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: Poisson summation formula
zbMATH Keywords: discrete moments condition
MaRDI profile type: Publication
full work available at URL: s00009-008-0137-2
OpenAlex ID: W1968676867
DOI: 10.1007/S00009-008-0137-2
description: scientific article; zbMATH DE number 5292749