title: Sharp estimates for mean square approximations of classes of differentiable periodic functions by shift spaces
metadata.name: dc.contributor.author
metadata.value: Vinogradov, Oleg L.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ulitskaya, Anastasiya Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-26T09:17:54Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-26T09:17:54Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vinogradov O.L., Ulitskaya A.Yu. Sharp estimates for mean square approximations of classes of differentiable periodic functions by shift spaces. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 1, pp. 22–31.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.103
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9495
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let L2 be the space of 2 -periodic square integrable functions; E(f,X)2 is the best
  approximation of the function f by the space X in L2. For n ∈ N, B ∈ L2 we denote
  by SB,n the space of functions s of the form
  s(x) =
  2n−1
  Xj=0
   jB  x −
  j 
  n  .
  In this paper, we give a description of all spaces SB,n for which the sharp inequality
  E(f, SB,n)2 6
  1
  nr kf(r)k2
  holds. In doing so, we indicate the subspaces of dimension 2n − 1 that provide the same
  estimate. The well-known inequalities for approximation by trigonometric polynomials and
  splines are obtained as particular cases.
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 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: best approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: shift spaces
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: sharp constants
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Sharp estimates for mean square approximations of classes of differentiable periodic functions by shift spaces
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 03-Vinogradov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9495/1/03-Vinogradov.pdf
resources.format: Adobe PDF
resources.size: 328,81 kB