Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101580
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dc.contributor.authorLeont'eva, A. O.en
dc.date.accessioned2021-08-31T14:58:15Z-
dc.date.available2021-08-31T14:58:15Z-
dc.date.issued2019-
dc.identifier.citationLeont'eva A. O. Bernstein-Szegõ inequality for trigonometric polynomials in the space L0 / A. O. Leont'eva. — DOI 10.21538/0134-4889-2019-25-4-129-135 // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2019. — Vol. 25. — Iss. 4. — P. 129-135.en
dc.identifier.issn1344889-
dc.identifier.otherFinal2
dc.identifier.otherAll Open Access, Bronze3
dc.identifier.otherhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85078517332&doi=10.21538%2f0134-4889-2019-25-4-129-135&partnerID=40&md5=75066690cbef48b51427786ba5c6ba55
dc.identifier.otherhttp://journal.imm.uran.ru/sites/default/files/content/25_4/TrIMMUrORAN_2019_4_p129_L.pdfm
dc.identifier.urihttp://hdl.handle.net/10995/101580-
dc.description.abstractInequalities of the form kfn (α) cos θ + fn (α) sin θkp ≤ Bn(α, θ)pkfnkp for classical derivatives of order α ∈ N and Weyl derivatives of real order α ≥ 0 of trigonometric polynomials fn of order n ≥ 1 and their conjugates for real θ and 0 ≤ p ≤ ∞ are called Bernstein-Szegõ inequalities. They are generalizations of the classical Bernstein inequality (α = 1, θ = 0, p = ∞). Such inequalities have been studied for more than 90 years. The problem of studying the Bernstein-Szegõ inequality consists in analyzing the properties of the best (the smallest) constant Bn(α, θ)p, its exact value, and extremal polynomials for which this inequality turns into an equality. G. Szegõ (1928), A. Zygmund (1933), and A. I. Kozko (1998) showed that, in the case p ≥ 1 for real α ≥ 1 and any real θ, the best constant Bn(α, θ)p is nα. For p = 0, Bernstein-Szegõ inequalities are of interest at least because the constant Bn(α, θ)p is the largest for p = 0 over 0 ≤ p ≤ ∞. In 1981, V. V. Arestov proved that, for r ∈ N and θ = 0, the Bernstein inequality is true with the constant nr in the spaces Lp, 0 ≤ p < 1; i.e., Bn(r, 0)p = nr. In 1994, he proved that, for p = 0 and the derivative of the conjugate polynomial of order r ∈ N ∪ {0}, i.e., for θ = π/2, the exact constant grows exponentially in n; more precisely, Bn(r, π/2)0 = 4n+o(n). In two recent papers of the author (2018), a similar result was obtained for Weyl derivatives of positive noninteger order for any real θ. In the present paper, we prove that the formula Bn(α, θ)0 = 4n+o(n) holds for derivatives of nonnegative integer orders α and any real θ 6= πk, k ∈ Z. © 2019 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.en
dc.format.mimetypeapplication/pdfen
dc.language.isoruen
dc.publisherKrasovskii Institute of Mathematics and Mechanicsen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceTr. Inst. Mat. Meh. UrO RAN2
dc.sourceTrudy Instituta Matematiki i Mekhaniki UrO RANen
dc.subjectBERNSTEIN-SZEGÕ INEQUALITYen
dc.subjectCONJUGATE POLYNOMIALen
dc.subjectSPACEL0en
dc.subjectTRIGONOMETRIC POLYNOMIALen
dc.subjectWEYL DERIVATIVEen
dc.titleBernstein-Szegõ inequality for trigonometric polynomials in the space L0en
dc.titleНеравенство Бернштейна - Сеге в пространстве L0 для тригонометрических полиномовru
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.doi10.21538/0134-4889-2019-25-4-129-135-
dc.identifier.scopus85078517332-
local.contributor.employeeLeont'eva, A.O., Ural Federal University, Yekaterinburg, 620083, Russian Federation, Krasovskii Institute of Mathematics, Mechanics of the Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620108, Russian Federation
local.description.firstpage129-
local.description.lastpage135-
local.issue4-
local.volume25-
local.contributor.departmentUral Federal University, Yekaterinburg, 620083, Russian Federation
local.contributor.departmentKrasovskii Institute of Mathematics, Mechanics of the Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620108, Russian Federation
local.identifier.pure11465023-
local.identifier.eid2-s2.0-85078517332-
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