Support curves of invertible Radon transforms
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 transfor...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
1993
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| Sorozat: | ARCHIV DER MATHEMATIK
61 No. 5 |
| doi: | 10.1007/BF01207544 |
| mtmt: | 1118117 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/15959 |
| LEADER | 01449nab a2200205 i 4500 | ||
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| 008 | 190703s1993 hu o 0|| angol d | ||
| 022 | |a 0003-889X | ||
| 024 | 7 | |a 10.1007/BF01207544 |2 doi | |
| 024 | 7 | |a 1118117 |2 mtmt | |
| 040 | |a SZTE Publicatio Repozitórium |b hun | ||
| 041 | |a angol | ||
| 100 | 1 | |a Kurusa Árpád | |
| 245 | 1 | 0 | |a Support curves of invertible Radon transforms |h [elektronikus dokumentum] / |c Kurusa Árpád |
| 260 | |c 1993 | ||
| 300 | |a 448-458 | ||
| 490 | 0 | |a ARCHIV DER MATHEMATIK |v 61 No. 5 | |
| 520 | 3 | |a 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. | |
| 856 | 4 | 0 | |u http://publicatio.bibl.u-szeged.hu/15959/1/supcur.pdf |z Dokumentum-elérés |