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Sibirsk. Mat. Zh., 2014, Volume 55, Number 3, Pages 592–609 (Mi smj2556)  

On reconstruction of multiplicative transformations of functions in anisotropic spaces

E. D. Nursultanovab, N. T. Tleukhanovab

a Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan
b Eurasian National University, Astana, Kazakhstan

Abstract: We construct a reconstruction operator for multiplicative transformations of functions in anisotropic spaces from their values at a given number of points. We show that the error of the reconstruction of a function in $W^\alpha_p$ coincides in order with the corresponding orthodiameter.

Keywords: operator of reconstruction of functions, space with dominating mixed derivative, orthodiameter.

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English version:
Siberian Mathematical Journal, 2014, 55:3, 482–497

Bibliographic databases:

UDC: 517.5
Received: 02.04.2012
Revised: 02.07.2013

Citation: E. D. Nursultanov, N. T. Tleukhanova, “On reconstruction of multiplicative transformations of functions in anisotropic spaces”, Sibirsk. Mat. Zh., 55:3 (2014), 592–609; Siberian Math. J., 55:3 (2014), 482–497

Citation in format AMSBIB
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\paper On reconstruction of multiplicative transformations of functions in anisotropic spaces
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 3
\pages 592--609
\mathnet{http://mi.mathnet.ru/smj2556}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3237376}
\elib{http://elibrary.ru/item.asp?id=21800675}
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\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 3
\pages 482--497
\crossref{https://doi.org/10.1134/S0037446614030100}
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