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Sbornik: Mathematics, 2022, Volume 213, Issue 3, Pages 385–411
DOI: https://doi.org/10.1070/SM9475 (Mi sm9475) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Optimal recovery in weighted spaces with homogeneous weights

K. Yu. Osipenkoabc

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
c Moscow Aviation Institute (National Research University), Moscow, Russia
English version PDF (563 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM9475
Abstract: The paper concerns problems of the recovery of operators from noisy information in weighted $L_q$-spaces with homogeneous weights. A number of general theorems are proved and applied to problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of the Laplace operator from a noisy Fourier transform in the $L_p$-metric.
Bibliography: 30 titles.
Keywords: optimal recovery, linear operator, Fourier transform, Carlson's inequality.
Received: 28.06.2020 and 12.12.2021
Russian version:
Matematicheskii Sbornik, 2022, Volume 213, Number 3, Pages 111–138
DOI: https://doi.org/10.4213/sm9475
Bibliographic databases:
Document Type: Article
MSC: 41A65, 41A46, 49N30
Language: English
Original paper language: Russian
Citation: K. Yu. Osipenko, “Optimal recovery in weighted spaces with homogeneous weights”, Mat. Sb., 213:3 (2022), 111–138; Sb. Math., 213:3 (2022), 385–411
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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