title: Optimal subspaces for mean square approximation of classes of differentiable functions on a segment
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: 2020-09-10T13:29:27Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-09-10T13:29:27Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vinogradov O. L., Ulitskaya A. Yu. Optimal subspaces for mean square approximation of classes of differentiable functions on a segment. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 3, pp. 404–417
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.304
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19391
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, we specify a set of optimal subspaces for L2 approximation of three classes
  of functions in the Sobolev spaces W
  (r)
  2
  , defined on a segment and subject to certain
  boundary conditions. A subspace X of dimension not exceeding n is called optimal for a
  function class A if the best approximation of A by X equals the Kolmogorov n-width of A.
  These boundary conditions correspond to subspaces of periodically extended functions with symmetry properties. All of the approximating subspaces are generated by equidistant shifts
  of a single function. The conditions of optimality are given in terms of Fourier coefficients
  of a generating function. In particular, we indicate optimal spline spaces of all degrees
  d > r − 1 with equidistant knots of several different types.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by the Russian Science Foundation under grant no. 18-11-00055.
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: spaces of shifts
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: splines
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: n-widths
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Optimal subspaces for mean square approximation of classes of differentiable functions on a segment
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 404-417.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19391/1/404-417.pdf
resources.format: Adobe PDF
resources.size: 352,62 kB