%0 Journal Article
%@ 0003-889X
%A  Kurusa Árpád
%A Bolyai Intézet (Matematikai Tanszékcsoport) SZTE / TTIK MTCS [2007-2015],
%D 1993
%F publicatio:15959
%J ARCHIV DER MATHEMATIK
%N 5
%P 448-458
%T Support curves of invertible Radon transforms
%U http://publicatio.bibl.u-szeged.hu/15959/
%V 61
%X 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.
%Z MR1241050 (94m:44001)