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Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 1, Pages 18–28 (Mi ivm9426)  

On approximation of non-analytic functions by analytical ones

H. H. Burchaeva, G. Y. Ryabykhb

a Chechen State University, 17a Dudaev blvd., Grozny, 364000 Russia
b Don State Technical University, 1 Gagarin Sq., Rostov-on-Don, 344000 Russia

Abstract: We study the properties of the elements of best approximation for functions summed up over the unit circle of functions by functions from the Bergman space. For approximable functions of a special type, we five a sufficiently accurate description of the properties of these elements in terms of the Hardy and Lipschitz classes. The result obtained is based on an analysis of the corresponding duality relation for extremal problems. The developed method is also applicable to relatively smooth (in terms of Sobolev spaces) approximable functions.

Keywords: Bergman space, Hardy space, element of best approximation, linear functional, extremal problems.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00017_а


DOI: https://doi.org/10.26907/0021-3446-2019-1-18-28

Full text: PDF file (231 kB)
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UDC: 517.53
Received: 09.12.2017
Revised: 09.12.2017
Accepted: 22.03.2018

Citation: H. H. Burchaev, G. Y. Ryabykh, “On approximation of non-analytic functions by analytical ones”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 1, 18–28

Citation in format AMSBIB
\Bibitem{BurRya19}
\by H.~H.~Burchaev, G.~Y.~Ryabykh
\paper On approximation of non-analytic functions by analytical ones
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2019
\issue 1
\pages 18--28
\mathnet{http://mi.mathnet.ru/ivm9426}
\crossref{https://doi.org/10.26907/0021-3446-2019-1-18-28}


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