relation: http://publicatio.bibl.u-szeged.hu/15959/
title: Support curves of invertible Radon transforms
creator:  Kurusa Árpád
description: Let $S$ and the origin be different points of the closed curve $s$ in the plane. For any point $P$ there is exactly one orientation preserving similarity $A_P$ which fixes the origin and takes $S$ to $P$. The function transformation $$ _{s} f(P)=int_{A_{Ps}}f(X)d X$$ is said to be the Radon transform with respect to the {it support curve} $s$, where $d X$ is the arclength measure on $A_{Ps}$. The invertibility of $ _{s}$ is proved on a subspace of the $ct$ functions if $s$ has strictly convex distance function. The support theorem is shown on a subspace of the $lt$ functions for curves having exactly two cross points with any of the circles centered to the origin. Counterexample shows the necessity of this condition. Finally a generalization to higher dimensions and a continuity result are given.
date: 1993
type: Folyóiratcikk
type: PeerReviewed
format: text
identifier: http://publicatio.bibl.u-szeged.hu/15959/1/supcur.pdf
identifier:     Kurusa Árpád: Support curves of invertible Radon transforms.   ARCHIV DER MATHEMATIK, 61 (5).  pp. 448-458.  ISSN 0003-889X (1993)     
identifier: doi:10.1007/BF01207544
relation: 1118117
language: eng
relation: info:eu-repo/semantics/altIdentifier/doi/10.1007/BF01207544
rights: info:eu-repo/semantics/openAccess