A characterization of the Radon transform's range by a system of PDEs
Let $g$ be a compactly supported function of $d$-planes in ${opr}^n$. We prove that then $g$ is in the range of the Radon transform if and only if $g$ satisfies an ultrahyperbolic system of PDEs. We parameterize the $d$-planes by $d+1$ points $x_0,x_1,ldots,x_d$ on them and get the PDE $$left( {part...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
1991
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| Sorozat: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
161 No. 1 |
| doi: | 10.1016/0022-247X(91)90371-6 |
| mtmt: | 1118113 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/15963 |
| Tartalmi kivonat: | Let $g$ be a compactly supported function of $d$-planes in ${opr}^n$. We prove that then $g$ is in the range of the Radon transform if and only if $g$ satisfies an ultrahyperbolic system of PDEs. We parameterize the $d$-planes by $d+1$ points $x_0,x_1,ldots,x_d$ on them and get the PDE $$left( {partial ^2over partial x^k_ipartial x^l_j} -{partial ^2over partial x^l_ipartial x^k_j} ight) {g(x_0,x_1,ldots,x_d)over Vol{x_i-x_0}_{i=1,d}} = 0, $$ where $x^k_i$ denotes the $k-th$ coordinate of $x_i$. At the end we analyze in detail the case of $d=1$. |
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| Terjedelem/Fizikai jellemzők: | 218-226 |
| ISSN: | 0022-247X |