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Sbornik: Mathematics, 2014, Volume 205, Issue 10, Pages 1442–1472
DOI: https://doi.org/10.1070/SM2014v205n10ABEH004425 (Mi sm8330) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Optimal recovery of linear operators in non-Euclidean metrics

K. Yu. Osipenkoab

a Moscow State Aviation Technological University, Moscow
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
English version PDF (633 kB) Citations (15)
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DOI: https://doi.org/10.1070/SM2014v205n10ABEH004425
Abstract: The paper looks at problems concerning the recovery of operators from noisy information in non-Euclidean metrics. A number of general theorems are proved and applied to recovery problems for functions and their derivatives from the noisy Fourier transform. In some cases, a family of optimal methods is found, from which the methods requiring the least amount of original information are singled out.
Bibliography: 25 titles.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12447
14-01-00456
Received: 17.01.2014 and 01.07.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 10, Pages 77–106
DOI: https://doi.org/10.4213/sm8330
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 41A65, 41A46, 49N30
Language: English
Original paper language: Russian
Citation: K. Yu. Osipenko, “Optimal recovery of linear operators in non-Euclidean metrics”, Mat. Sb., 205:10 (2014), 77–106; Sb. Math., 205:10 (2014), 1442–1472
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm8330
  • https://doi.org/10.1070/SM2014v205n10ABEH004425
  • https://www.mathnet.ru/eng/sm/v205/i10/p77
    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:549
    Russian version PDF:201
    English version PDF:9
    References:62
    First page:34
     
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