title: Entire functions of order 1/2 in the approximation of functions on the semiaxis
metadata.name: dc.contributor.author
metadata.value: Silvanovich, Olga V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shirokov, Nikolai A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-12-06T12:49:38Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-12-06T12:49:38Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Silvanovich O.V., Shirokov N.A. Entire functions of order 1/2 in the approximation of functions on the semiaxis. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 4, pp. 627–635.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.408
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16745
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let In be disjoint segments of half-axis [1;1), I1 = [1; b1]. We assume that In and their supplementary intervals are commensurable. The union of mentioned segments we denote thought E. Let 0 < α< 1. The class of complex-valued functions defined on E with r-th derivative belonging to a Holder class α and bounded by 1 is denoted by H_1^(r+α)(E). We consider the set Cσ of entire functions of the order 1/2 and of the type ≤σ which are bounded on [0;1). The main result of this paper is the following: Let f∈ 2 H_1^(r+α)(E). Then there exist constants c0 and c1, depending of f,E, r and α such that for any σ≥ 1 one can find a function Fσ ∈ Cσ such that the following inequality holds |f(x) − Fσ(x)|≤ min(c0∙1/σr+α(√((x-a_n)(b_n )-x)+n/σ)r+α,c1), x ∈ In, n ≥ 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The article was prepared with the financial support of the Russian Foundation for Basic Research (RFBR), project No. 17-01-00607-а
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: smooth functions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: entire functions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: approximation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Entire functions of order 1/2 in the approximation of functions on the semiaxis
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 627-635.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16745/1/627-635.pdf
resources.format: Adobe PDF
resources.size: 304,55 kB