RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mosc. Math. J.: Year: Volume: Issue: Page: Find

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

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
\Bibitem{Nov14} \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} 

• http://mi.mathnet.ru/eng/mmj545
• http://mi.mathnet.ru/eng/mmj/v14/i4/p807

 SHARE:

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
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
3. F. O. Goncharov, “An iterative inversion of weighted Radon transforms along hyperplanes”, Inverse Probl., 33:12 (2017), 124005
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
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