|
This article is cited in 9 scientific papers (total in 9 papers)
Weighted Radon transforms and first order differential systems on the plane
R. G. Novikov CNRS (UMR 7641), Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France
Abstract:
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 $\mathbb R^2=\mathbb C$ with a decay condition at infinity. As a corollary, we obtain new injectivity and inversion results for weighted Radon transforms on the plane.
Key words and phrases:
weighted Radon transforms, inversion methods, first order differential systems.
Received: August 3, 2012; in revised form July 5, 2014
Citation:
R. G. Novikov, “Weighted Radon transforms and first order differential systems on the plane”, Mosc. Math. J., 14:4 (2014), 807–823
Linking options:
https://www.mathnet.ru/eng/mmj545 https://www.mathnet.ru/eng/mmj/v14/i4/p807
|
|