title: Estimates of the norm of a function orthogonal to piecewiseconstant functions by moduli of continuity of high order
metadata.name: dc.contributor.author
metadata.value: Vinogradov, Oleg L.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ikhsanov, Lev N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-09-01T14:55:11Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-01T14:55:11Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-03
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3832
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the paper, we estimate the uniform norm of a function defined on the real line and having zero integrals
  between integer points by its modulus of continuity of arbitrary even order. Sharp estimates of such
  kind are known for periodic functions. The passage to non-periodic functions essentially complicates the
  problem. In general, the constant for non-periodic functions is greater than for periodic ones. The constants
  in the estimate are improved in comparison with those known earlier. The estimates under discussion
  have something in common with the problem of finding the Whitney constants, i.e. the constants in the
  inequalities between the best approximations and the moduli of continuity of a function defined on the
  segment. The proof is based on the representation of the error of the polynomial interpolation as a product
  of the influence polynomial and the integrated difference of high order. We also obtain pointwise estimates
  in terms of moduli of continuity. Refs 5.
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: modulus of continuity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: interpolation in the mean
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Estimates of the norm of a function orthogonal to piecewiseconstant functions by moduli of continuity of high order
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Vinogradov_Ikhsanov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3832/1/Vinogradov_Ikhsanov.pdf
resources.format: Adobe PDF
resources.size: 204,9 kB