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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 293, Pages 201–216
DOI: https://doi.org/10.1134/S037196851602014X (Mi tm3714) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Exactness and optimality of methods for recovering functions from their spectrum

G. G. Magaril-Il'yaevabc, K. Yu. Osipenkocdb

a Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198 Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
c Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
d Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia
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DOI: https://doi.org/10.1134/S037196851602014X
Abstract: Optimal methods are constructed for recovering functions and their derivatives in a Sobolev class of functions on the line from exactly or approximately defined Fourier transforms of these functions on an arbitrary measurable set. The methods are exact on certain subspaces of entire functions. Optimal recovery methods are also constructed for wider function classes obtained as the sum of the original Sobolev class and a subspace of entire functions.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00456
14-01-00744
This work was supported by the Russian Foundation for Basic Research, project nos. 14-01-00456 and 14-01-00744.
Received: November 9, 2015
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 293, Pages 194–208
DOI: https://doi.org/10.1134/S0081543816040143
Bibliographic databases:
Document Type: Article
UDC: 517.984.64
Language: Russian
Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Exactness and optimality of methods for recovering functions from their spectrum”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 201–216; Proc. Steklov Inst. Math., 293 (2016), 194–208
Citation in format AMSBIB
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\paper Exactness and optimality of methods for recovering functions from their spectrum
\inbook Function spaces, approximation theory, and related problems of mathematical analysis
\bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii
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\vol 293
\pages 201--216
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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