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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 6, Pages 83–102 (Mi izv8182)  

On the best methods for recovering derivatives in Sobolev classes

G. G. Magaril-Il'yaevab, K. Yu. Osipenkoacb

a M. V. Lomonosov Moscow State University
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
c Moscow State Aviation Technological University, Moscow

Abstract: We construct the best (optimal) methods for recovering derivatives of functions in generalized Sobolev classes of functions on $\mathbb R^d$ provided that for every such function we know (exactly or approximately) its Fourier transform on an arbitrary measurable set $A\subset\mathbb R^d$. In both cases we construct families of optimal methods. These methods use only part of the information about the Fourier transform, and this part is subject to some filtration. We consider the problem of finding the best set for the recovery of a given derivative among all sets of a fixed measure.

Keywords: optimal recovery, Sobolev class, extremal problem, Fourier transform.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12447
14-01-00456


DOI: https://doi.org/10.4213/im8182

Full text: PDF file (578 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2014, 78:6, 1138–1157

Bibliographic databases:

UDC: 517.984.64
MSC: 26D15, 42B10, 49K35, 90C47
Received: 25.10.2013

Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the best methods for recovering derivatives in Sobolev classes”, Izv. RAN. Ser. Mat., 78:6 (2014), 83–102; Izv. Math., 78:6 (2014), 1138–1157

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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