title: Approximation by entire functions on a countable set of continuums
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: 2020-09-10T14:52:00Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-09-10T14:52:00Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-10
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Silvanovich O. V., Shirokov N. A. Approximation by entire functions on a countable set of continuums. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 3, pp. 481–489.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.310
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19398
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider a problem of approximation by entire functions of exponential type of functions
  defined on a countable set E of continuums Gn, E =
  S
  n∈Z
  Gn. We assume that all Gn
  are pairwise disjoint and are situated near the real axis. We assume too that all Gn are commensurable in a sense and have uniformly smooth boundaries. A function f is defined
  independantly on each Gn and is bounded on E and f
  (r) has a module of continuity ω
  which satisfies a condition
  Zx
  0
  ω(t)
  t
  dt + x
  Z∞
  x
  ω(t)
  t
  2
  dt ≤ cω(x).
  Then we construct an entire function Fσ of exponential type ≤ σ such that we have the
  following estimate of approximation of the function f by functions Fσ:
  |f(z) − Fσ(z)| ≤ cf σ
  −r
  ω(σ
  −r
  ), z ∈ Z, σ ≥ 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work of N. A. Shirokov was supported by the Russian Foundation for Basic Research, project No 20-01-00209
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 7 (65); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: Hölder classes
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: entire functions of exponential type
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Approximation by entire functions on a countable set of continuums
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 481-489.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19398/1/481-489.pdf
resources.format: Adobe PDF
resources.size: 315,6 kB