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| HAL: hal-00714524, version 1 |
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| Weighted Radon transforms and first order differential systems on the plane |
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| Roman Novikov 1 |
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| (2012-07-04) |
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| We consider weighted Radon transforms on the plane, where weights are given as finite Fourier series in angle variable. By means of additive Riemann-Hilbert problem techniques, we reduce inversion of these transforms to solving first order differential systems on $\R^2=\C$ with a decay condition at infinity. As a corollary, we obtain new injectivity and inversion results for weighted Radon transforms on the plane. |
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| 1: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| Subject | : | Mathematics/Functional Analysis Mathematics/Analysis of PDEs |
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| hal-00714524, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00714524 | |
| oai:hal.archives-ouvertes.fr:hal-00714524 | |
| From: Roman Novikov | |
| Submitted on: Wednesday, 4 July 2012 20:22:29 | |
| Updated on: Wednesday, 4 July 2012 21:51:25 | |
