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Zapiski Nauchnykh Seminarov POMI, 1999, Volume 257, Pages 298–303 (Mi znsl1001)  
This article is cited in 1 scientific paper (total in 1 paper)

Reqularization problems in three-dimensional ray tomography

V. N. Troyan, G. A. Ryzhikov

Saint-Petersburg State University
Full-text PDF (113 kB) Citations (1)
Abstract: The connections between the Tikhonov's regularization, the statistical regularization and the potential theory are considered. It is demonstrated that the use of the Tikhonov's regularization leads to such a form of correlation operators that may be interpreted as potentials by Coulomb or Yukawa. It is given the physical interpretation of the ray interaction as “charged” strings with corresponding potentials.
Received: 26.08.1998
English version:
Journal of Mathematical Sciences (New York), 2002, Volume 108, Issue 5, Pages 859–862
DOI: https://doi.org/10.1023/A:1013271817538
Bibliographic databases:
UDC: 550.834
Language: Russian
Citation: V. N. Troyan, G. A. Ryzhikov, “Reqularization problems in three-dimensional ray tomography”, Mathematical problems in the theory of wave propagation. Part 28, Zap. Nauchn. Sem. POMI, 257, POMI, St. Petersburg, 1999, 298–303; J. Math. Sci. (New York), 108:5 (2002), 859–862
Citation in format AMSBIB
\Bibitem{TroRyz99}
\by V.~N.~Troyan, G.~A.~Ryzhikov
\paper Reqularization problems in three-dimensional ray tomography
\inbook Mathematical problems in the theory of wave propagation. Part~28
\serial Zap. Nauchn. Sem. POMI
\yr 1999
\vol 257
\pages 298--303
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1001}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1754705}
\zmath{https://zbmath.org/?q=an:1071.74609}
\transl
\jour J. Math. Sci. (New York)
\yr 2002
\vol 108
\issue 5
\pages 859--862
\crossref{https://doi.org/10.1023/A:1013271817538}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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