title: Approximation by entire functions on a countable union of segments on the real axis. 2. Proof of the main theorem
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: 2017-07-05T09:09:37Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-07-05T09:09:37Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-03
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. 2. Proof of the main theorem. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 1, pp. 53–63.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.108
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6687
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We proof 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. The set E ⊂ R consists of disjoint 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 and satisfying the condition
  |f(x) − f(y)| ≤ c0|x − y| , x, y ∈ [an, bn], 0 < α < 1. The construction of an approximation of f by
  entire functions we begin from a construction of a series of domains D+ and D− depending of sequens
  {x′}n∈Z and {x′′}n∈Z : x′
  n, x′′
  n ∈ [an, bn]. We introduce a special conformed mappings of D+ and D−
  to themselves and use these mapping to form kernels Rk(z,w, ξ, ζ).
  Afterwards we combine a continuation of a function f from the set E to the whole complex plane C
  from our first part of this paper and kernels Rk(z,w, ξ, ζ). We get as a result a series of entire functions
  of exponential type depending on sequences {x′
  n}n∈Z and {x′′
  n}n∈Z. Then we use sequences {x′
  n}n∈Z and
  {x′′
  n}n∈Z to construct a final approximating entire function F . Refs 3.
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 4 (62); Issue 1
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. 2. Proof of the main theorem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 08-Silvanovich.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6687/1/08-Silvanovich.pdf
resources.format: Adobe PDF
resources.size: 276,73 kB