TY  - JOUR
SP  - 448
Y1  - 1993///
N2  - 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.
EP  - 458
N1  - MR1241050 (94m:44001)
JF  - ARCHIV DER MATHEMATIK
VL  - 61
IS  - 5
ID  - publicatio15959
UR  - http://publicatio.bibl.u-szeged.hu/15959/
SN  - 0003-889X
AV  - public
TI  - Support curves of invertible Radon transforms
A1  -  Kurusa Árpád
ER  -