Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111132
Title: Approximation of Derivatives of Analytic Functions from One Hardy Class by Another Hardy Class
Authors: Akopyan, R. R.
Issue Date: 2020
Publisher: Pleiades journals
Pleiades Publishing Ltd
Citation: Akopyan R. R. Approximation of Derivatives of Analytic Functions from One Hardy Class by Another Hardy Class / R. R. Akopyan // Proceedings of the Steklov Institute of Mathematics. — 2020. — Vol. 308. — P. 1-8.
Abstract: In the Hardy space Hp(Dϱ), 1 ≤ p ⪯ ∞, of functions analytic in the disk Dϱ = {z ∈ ℂ}: z < ϱ, we denote by NHp(Dϱ), N > 0, the class of functions whose Lp-norm on the circle γϱ = {z ∈ ℂ: z = ϱ} does not exceed the number N and by ∂Hp(Dϱ) the class consisting of the derivatives of functions from 1Hp(Dϱ). We consider the problem of the best approximation of the class ∂Hp(Dϱ) by the class NHp(DR)N > 0, with respect to the Lp-norm on the circle γr, 0 < r < ρ < R. The order of the best approximation as N → +∞ is found: (Formula presented.) In the case where the parameter N belongs to some sequence of intervals, the exact value of the best approximation and a linear method implementing it are obtained. A similar problem is considered for classes of functions analytic in annuli. © 2020, Pleiades Publishing, Ltd.
Keywords: ANALYTIC FUNCTIONS
BEST APPROXIMATION OF A CLASS BY A CLASS
HARDY CLASS
URI: http://hdl.handle.net/10995/111132
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85085381000
PURE ID: 12922046
ISSN: 0081-5438
metadata.dc.description.sponsorship: This work was supported by the Russian Foundation for Basic Research (project no. 18-01-00336) and by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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