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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1295–1309 (Mi smj1256)  

This article is cited in 1 scientific paper (total in 1 paper)

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

A. S. Leonov

Moscow Engineering Physics Institute (State University)

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

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English version:
Siberian Mathematical Journal, 2003, 44:6, 1015–1026q

Bibliographic databases:

UDC: 514.13
Received: 19.02.2002

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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\by A.~S.~Leonov
\paper General regularizing functionals for solving ill-posed problems in Lebesgue spaces
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1295--1309
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034936}
\zmath{https://zbmath.org/?q=an:1046.47051}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 1015--1026q
\crossref{https://doi.org/10.1023/B:SIMJ.0000007477.31754.b6}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187464000009}


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    This publication is cited in the following articles:
    1. Bazulin A.E., Bazulin E.G., “The possibility of using the maximum–entropy method in ultrasonic nondestructive testing for increasing the resolution of echo signals”, Russian Journal of Nondestructive Testing, 42:9 (2006), 559–577  crossref  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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