title: Approximation by entire functions on a countable union of segments on the real axis
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: 2017-01-05T18:10:14Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-01-05T18:10:14Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Silvanovich O.V., Shirokov N.A. Approximation by entire functions on a countable union of segments on the real axis. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 4, pp. 644–650.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.414
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/5905
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We state in the present paper a theorem about approximation of a function defined on a countable union
  of segments of the real line by means of entire functions of exponential type. The approximating function
  is supposed to belong to a Holder class α, 0 < α< 1, and the rate of approximation turns out to be better
  in a vicinity of ends of segments similary to the case of case of polynomial approximation of a function on
  one segment.
  Now, we consider a set E ⊂ R consisting of disjonct segments [an, bn], −∞ < n < +∞ such that
  bn − an   bk − ak for any n and k and an+1 − bn   bn − an for any n. The function f defined on
  E supposed to be bounded by a constant M on all of segments [an, bn] and satisfying the condition
  |f(x) − f(y)| ≤ c0|x − y|α, x, y ∈ [an, bn], 0 < α < 1. For σ ≥ 1, ξ = 1
  σ , x ∈ [an, bn] we define a scale of
  approximation d1+ξ(x, [an, bn]) such that d1+ξ(x, [an, bn])   ξ(ξ2 + min(x − an)2, (bn − x)2)
  1
  2 . Then the
  main theorem states that there exists a constant c1 depending only on f and E such that we can find a
  function Fσ of exponential type ≤ σ which approximate a function f in a following way:
  |Fσ(x) − f(x)| ≤ c1dα
  1+ξ(x, [an, bn]), x ∈ [an, bn].
  Refs 4.
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Holder classe σ
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: entire function of exponential type
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: approximation on subsets of real line
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Approximation by entire functions on a countable union of segments on the real axis
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 14-Silvanovich.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/5905/1/14-Silvanovich.pdf
resources.format: Adobe PDF
resources.size: 242,43 kB