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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 242–246 (Mi mz3794)  

This article is cited in 4 scientific papers (total in 4 papers)

On a Sufficient Condition for Regularizability of Linear Inverse Problem

L. D. Menikhes

South Ural State University

Abstract: We study the regularizability of mappings inverse to continuous linear operators from $C(0,1)$ into $L_2(0,1)$ and obtain a sufficient condition for the regularizability of such mappings in terms of the properties of the extended operator. We show that the obtained condition is in a sense exact.

Keywords: linear inverse problem, continuous linear operator, integral operator, regularization, Banach space, locally convex space

DOI: https://doi.org/10.4213/mzm3794

Full text: PDF file (380 kB)
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English version:
Mathematical Notes, 2007, 82:2, 212–215

Bibliographic databases:

UDC: 517.9
Received: 21.08.2002
Revised: 09.11.2006

Citation: L. D. Menikhes, “On a Sufficient Condition for Regularizability of Linear Inverse Problem”, Mat. Zametki, 82:2 (2007), 242–246; Math. Notes, 82:2 (2007), 212–215

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Tabarintseva, “Ob otsenke pogreshnosti metoda priblizhennogo resheniya obratnoi zadachi dlya polulineinogo differentsialnogo uravneniya”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:3 (2013), 85–94  mathnet
    2. L. D. Menikhes, “O svyazi dostatochnykh uslovii regulyarizuemosti integralnykh uravnenii”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 5:1 (2013), 50–54  mathnet
    3. V. V. Karachik, “Ob odnoi neklassicheskoi zadache dlya uravneniya Gelmgoltsa”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 6:3 (2014), 14–22  mathnet
    4. L. D. Menikhes, V. V. Karachik, “On the regularizability conditions of integral equations”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:3 (2015), 141–147  mathnet  crossref  elib
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