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Moscow Mathematical Journal, 2014, Volume 14, Number 4, Pages 807–823
DOI: https://doi.org/10.17323/1609-4514-2014-14-4-807-823
(Mi mmj545)
 

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
Full-text PDF Citations (9)
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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
Bibliographic databases:
Document Type: Article
MSC: 44A12, 53C65, 65R10
Language: English
Citation: R. G. Novikov, “Weighted Radon transforms and first order differential systems on the plane”, Mosc. Math. J., 14:4 (2014), 807–823
Citation in format AMSBIB
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\by R.~G.~Novikov
\paper Weighted Radon transforms and first order differential systems on the plane
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 4
\pages 807--823
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3292050}
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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