title: Approximation by entire functions on a countable union of segments on the real axis. 3. Further generalization
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: 2018-07-12T19:38:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-12T19:38:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
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. 3. Further generalization. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 2, pp. 270–277.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.207
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10404
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the present paper we consider the approximation of smooth functions from various classes
  with the help of entire functions of exponential type. We assume that our smooth functions
  f are defined on an union of countable set of segments {[an; bn]} lying on the real axis
  such that all of those segments are commensurable and all complementary intervals are
  commensurable too. Let ! be a modulus of continuity satisfying a classical Dini condition,
  namely
  x
  Z
  0
  !(t)
  t
  dt + x
  ∞
  Z
  x
  !(t)
  t2 dt   c · !(x).
  We consider classes of functions f such that f is bounded on S n∈Z
  [an; bn] and for all r   0,
  x1, x2 2 In one has a property |f(r)(x2) − f(r)(x1)|   cf!(|x2 − x1|), f(0) def
  = f. We denote
  through T  a set of entire functions of exponential type     bounded on the real axis. The
  main result of our paper is following.
  Theorem. Let a function f and a modulus of continuity ! satisfy conditions mentioned
  above. Then for any     1 there exists a function F  2 T  such that for x 2 S n∈Z
  [an; bn]
  one has an estimate
  |f(x) − F (x)|   cf dr
  1+ 1
   
  (x, [n∈Z
  [an; bn])!(d1+ 1
   
  (x, [n∈Z
  [an; bn])),
  where characteristic d (x, . . .) was introduced in our paper (Vestnik St.Petersburg Univ.:
  Math. 49, issue 4, 373–378 (2016)).
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 5(63); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: smooth functions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: entire functions 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. 3. Further generalization
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Silvanovich.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10404/1/07-Silvanovich.pdf
resources.format: Adobe PDF
resources.size: 300,27 kB