Geodesic
On optimal recovery of values of linear operators from information known with a~stochastic error
Sbornik. Mathematics, Tome 212 (2021) no. 11, pp. 1588-1607

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The optimal recovery of values of linear operators is considered for classes of elements the information on which is known with a stochastic error. Linear optimal recovery methods are constructed that, in general, do not use all the available information for the measurements. As a consequence, an optimal method is described for recovering a function from a finite set of its Fourier coefficients specified with a stochastic error. Bibliography: 14 titles.
Keywords: optimal recovery, minimax estimation, extremal problem, linear operator.
Mots-clés : Fourier coefficients 
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     author = {K. Yu. Krivosheev},
     title = {On optimal recovery of values of linear operators from information known with a~stochastic error},
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K. Yu. Krivosheev. On optimal recovery of values of linear operators from information known with a~stochastic error. Sbornik. Mathematics, Tome 212 (2021) no. 11, pp. 1588-1607. http://geodesic.mathdoc.fr/item/SM_2021_212_11_a3/