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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 4, Pages 739–755
(Mi smj1874)
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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
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
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
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https://www.mathnet.ru/eng/smj1874 https://www.mathnet.ru/eng/smj/v49/i4/p739
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Abstract page: | 320 | Full-text PDF : | 97 | References: | 57 |
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