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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 1, Pages 18–28
DOI: https://doi.org/10.26907/0021-3446-2019-1-18-28 (Mi ivm9426) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
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DOI: https://doi.org/10.26907/0021-3446-2019-1-18-28
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
Supported by Russian Foundation for Basic Research, grant No. 18-01-00017.
Received: 09.12.2017
Revised: 09.12.2017
Accepted: 22.03.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 1, Pages 14–23
DOI: https://doi.org/10.3103/S1066369X1901002X
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
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; Russian Math. (Iz. VUZ), 63:1 (2019), 14–23
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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