Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101473
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dc.contributor.authorAkishev, G.en
dc.date.accessioned2021-08-31T14:57:33Z-
dc.date.available2021-08-31T14:57:33Z-
dc.date.issued2020-
dc.identifier.citationAkishev G. Estimates of best approximations of functions with logarithmic smoothness in the lorentz space with anisotropic norm / G. Akishev. — DOI 10.15826/umj.2020.1.002 // Ural Mathematical Journal. — 2020. — Vol. 6. — Iss. 1. — P. 16-29.en
dc.identifier.issn24143952-
dc.identifier.otherFinal2
dc.identifier.otherAll Open Access, Gold, Green3
dc.identifier.otherhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85089116548&doi=10.15826%2fumj.2020.1.002&partnerID=40&md5=2938d467518173b8f9443797f4a6b8e8
dc.identifier.otherhttps://umjuran.ru/index.php/umj/article/download/210/pdfm
dc.identifier.urihttp://hdl.handle.net/10995/101473-
dc.description.abstractIn this paper, we consider the anisotropic Lorentz space L∗¯p, ¯θ (Im) of periodic functions of m variables. The Besov space B(0,α,τ)¯p, ¯θ of functions with logarithmic smoothness is defined. The aim of the paper is to find an exact order of the best approximation of functions from the class B(0,α,τ)¯p, ¯θ by trigonometric polynomials under different relations between the parameters ¯p, ¯θ, and τ . The paper consists of an introduction and two sections. In the first section, we establish a sufficient condition for a function f ∈ L∗¯p,¯θ(1) (Im) to belong to the space L∗¯p,θ(2) (Im) in the case 1< θ2 < θj(1), j = 1, …, m, in terms of the best approximation and prove its unimprovability on the class Eλ¯p, ¯θ = {f ∈ L∗¯p,¯θ (Im): En(f)¯p,¯θ ≤ λn, n = 0, 1, …}, where En(f)¯p, ¯θ is the best approximation of the function f ∈ L∗¯p,¯θ (Im) by trigonometric polynomials of order n in each variable xj, j = 1, …, m, and λ = {λn} is a sequence of positive numbers λn ↓ 0 as n → +∞. In the second section, we establish order-exact estimates for the best approximation of functions from the class B(0,α,τ)¯p, ¯θ(1) in the space L∗¯p,θ(2) (Im). © 2020, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences. All rights reserved.en
dc.description.sponsorshipThis work was supported by the Competitiveness Enhancement Program of the Ural Federal University (Enactment of the Government of the Russian Federation of March 16, 2013 no. 211, agreement no. 02.A03. 21.0006 of August 27, 2013).en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciencesen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceUral Math. J.2
dc.sourceUral Mathematical Journalen
dc.subjectBEST APPROXIMATIONen
dc.subjectLORENTZ SPACEen
dc.subjectNIKOL’SKII–BESOV CLASSen
dc.titleEstimates of best approximations of functions with logarithmic smoothness in the lorentz space with anisotropic normen
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.doi10.15826/umj.2020.1.002-
dc.identifier.scopus85089116548-
local.contributor.employeeAkishev, G., L.N. Gumilyov Eurasian National University, 2 Pushkin str, Nur-Sultan, 010008, Kazakhstan, Ural Federal University, 19 Mira str, Ekaterinburg, 620002, Russian Federation
local.description.firstpage16-
local.description.lastpage29-
local.issue1-
local.volume6-
local.contributor.departmentL.N. Gumilyov Eurasian National University, 2 Pushkin str, Nur-Sultan, 010008, Kazakhstan
local.contributor.departmentUral Federal University, 19 Mira str, Ekaterinburg, 620002, Russian Federation
local.identifier.pure13679248-
local.identifier.pure6e9740cc-fdfc-4e15-97dc-d9fe7010175euuid
local.identifier.eid2-s2.0-85089116548-
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