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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 6, Pages 1295–1309 (Mi smj1256)  
This article is cited in 3 scientific papers (total in 3 papers)

General regularizing functionals for solving ill-posed problems in Lebesgue spaces

A. S. Leonov

Moscow Engineering Physics Institute (State University)
Full-text PDF (242 kB) Citations (3)
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Abstract: We study sufficient conditions for general integral functionals in Lebesgue spaces to possess regularizing properties required for solving nonlinear ill-posed problems. We select special classes of such functionals: uniformly convex and quasiuniformly convex (in the extended sense). We give a series of examples and, in particular, a functional that can be used in a generalized version of the maximum entropy method in Lebesgue spaces.
Keywords: regularization, ill-posed problem, Lebesgue space, uniformly (quasiuniformly) convex functional, $H$-property, maximum entropy method.
Received: 19.02.2002
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 6, Pages 1015–1026q
DOI: https://doi.org/10.1023/B:SIMJ.0000007477.31754.b6
Bibliographic databases:
UDC: 514.13
Language: Russian
Citation: A. S. Leonov, “General regularizing functionals for solving ill-posed problems in Lebesgue spaces”, Sibirsk. Mat. Zh., 44:6 (2003), 1295–1309; Siberian Math. J., 44:6 (2003), 1015–1026q
Citation in format AMSBIB
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\pages 1295--1309
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\transl
\jour Siberian Math. J.
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\issue 6
\pages 1015--1026q
\crossref{https://doi.org/10.1023/B:SIMJ.0000007477.31754.b6}
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    • This publication is cited in the following 3 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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