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Mosc. Math. J., 2014, Volume 14, Number 4, Pages 807–823 (Mi mmj545)  

This article is cited in 5 scientific papers (total in 5 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.

DOI: https://doi.org/10.17323/1609-4514-2014-14-4-807-823

Full text: http://www.mathjournals.org/.../2014-014-004-007.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 44A12, 53C65, 65R10
Received: August 3, 2012; in revised form July 5, 2014
Language:

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
\mathnet{http://mi.mathnet.ru/mmj545}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-4-807-823}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3292050}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000349324800007}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. Ilmavirta, “Coherent quantum tomography”, SIAM J. Math. Anal., 48:5 (2016), 3039–3064  crossref  mathscinet  zmath  isi  scopus
    2. F. Monard, “Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces”, SIAM J. Math. Anal., 48:2 (2016), 1155–1177  crossref  mathscinet  zmath  isi  scopus
    3. F. O. Goncharov, “An iterative inversion of weighted Radon transforms along hyperplanes”, Inverse Probl., 33:12 (2017), 124005  crossref  mathscinet  zmath  isi  scopus
    4. F. O. Goncharov, R. G. Novikov, “An example of non-uniqueness for Radon transforms with continuous positive rotation invariant weights”, J. Geom. Anal., 28:4 (2018), 3807–3828  crossref  mathscinet  zmath  isi  scopus
    5. F. O. Goncharov, R. G. Novikov, “An example of non-uniqueness for the weighted Radon transforms along hyperplanes in multidimensions”, Inverse Probl., 34:5 (2018), 054001  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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