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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 4, Pages 739–755 (Mi smj1874)  

This article is cited in 10 scientific papers (total in 10 papers)

The indicator of contact boundaries for an integral geometry problem

D. S. Anikonov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: We pose and study a rather particular integral geometry problem. In the two-dimensional space we consider all possible straight lines that cross some domain. The known data consist of the integrals over every line of this kind of an unknown piecewise smooth function that depends on both points of the domain and the variables characterizing the lines. The object we seek is the discontinuity curve of the integrand. This problem arose in the author's previous research in X-ray tomography. In essence, it is a generalization of one mathematical aspect of flaw detection theory, but seems of interest in its own right. The main result of this article is the construction of a special function that can be unbounded only near the required curve. Precisely for this reason we call the function the indicator of contact boundaries. A uniqueness theorem for the solution follows rather easily from the property of indicators.
Keywords: integral geometry, inverse problem, singular integral, tomography.
Received: 26.02.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 4, Pages 587–600
DOI: https://doi.org/10.1007/s11202-008-0056-2
Bibliographic databases:
UDC: 517.958
Language: Russian
Citation: D. S. Anikonov, “The indicator of contact boundaries for an integral geometry problem”, Sibirsk. Mat. Zh., 49:4 (2008), 739–755; Siberian Math. J., 49:4 (2008), 587–600
Citation in format AMSBIB
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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