Range of the horocyclic Radon transform on trees
type: Item
instance of: scholarly article
title: Range of the horocyclic Radon transform on trees
zbMATH Open document ID: 0944.44002
author: Enrico Casadio Tarabusi
author: Joel M. Cohen
author: Flavia Colonna
publication date: 2000-03-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75414
review text: The authors describe the range of the horocyclic Radon transform \(R\) on a homogeneous tree \(T\). They first state the two Radon conditions, families of natural explicit relations for functions on the space \({\mathcal H}\) of horocycles of \(T\). They then show that, among compactly supported functions on \({\mathcal H}\), these conditions completely characterize the range of \(R\) on finitely supported functions on (the set of vertices of) \(T\). Similar descriptions are valid for the range of \(R\) on larger function spaces, although distributions on \({\mathcal H}\) need then to be taken into account. One of the theorems states that for \(s<1/\sqrt q\) the Radon transform is one-to-one on \(A_s\) and its range is \(B_s\).
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1409069
zbMATH Keywords: Radon transform
zbMATH Keywords: homogeneous trees
zbMATH Keywords: horocycles
zbMATH Keywords: range characterization
zbMATH Keywords: distributions
MaRDI profile type: Publication
OpenAlex ID: W2326122176
cites work: Integral Geometry in Hyperbolic Spaces and Electrical Impedance Tomography
cites work: Integral Geometry on Trees
cites work: An inversion formula for the Radon transform on trees
cites work: Q3743818
cites work: Characterization of the range of the Radon transform on homogeneous trees
cites work: The horocyclic Radon transform on non-homogeneous trees
cites work: The functional analysis of the X-ray transform on trees
cites work: The radial Fourier-Stieltjes algebra of free groups
cites work: An overview of harmonic analysis on the group of isometries of a homogeneous tree
cites work: The range of the Helgason-Fourier transformation on homogeneous trees
cites work: The Radon transform
DOI: 10.5802/AIF.1752
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1409069