Moscow Mathematical Journal

Volume 14, Issue 4, October–December 2014 pp. 807–823.

Weighted Radon Transforms and First Order Differential Systems on the Plane

Authors: R. G. Novikov
Author institution:CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau, France;
IEPT RAS, Moscow, Russia

Summary:

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 ℝ²=ℂ with a decay condition at infinity. As a corollary, we obtain new injectivity and inversion results for weighted Radon transforms on the plane.

2010 Mathematics Subject Classification. 44A12, 53C65, 65R10

Keywords: Weighted Radon transforms, inversion methods, first order differential systems

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