title: Double-sided to Lebesgue function of Fourier sums by polynomials orthogonal on non-uniform grids
metadata.name: dc.contributor.author
metadata.value: Nurmagomedov, Alim A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Rasulov, Nabiyullah K.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:39:08Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:39:08Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Nurmagomedov A.A., Rasulov N.K. Double-sided to Lebesgue function of Fourier sums by polynomials orthogonal on non-uniform grids. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 417–430.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.306
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14885
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let Ω = {t0, t1, . . . , tN} and ΩN = {x0, x1, . . . , xN−1}, where xj = (tj + tj+1)/2, j =
  0, 1, . . . , N − 1 are any systems of different points from [−1, 1]. For arbitrary continuous
  function f(x) on the segment [−1, 1] discrete Fourier sums is constructed by a system
  of polynomials {ˆpk,N(x)}N−1
  k=0 forming an orthonormal system on non-uniform system of
  points ΩN consisting of a finite number of N points from segment [−1, 1] with weight
  Δtj = tj+1 − tj . We have found an order for Lebesgue function Ln,N(x) of the growing
  discrete Fourier sums Sn,N(f, x) for n = O(δ
  −2/7
  N ), δN = max0
  ≤j≤N−1 Δtj. Namely, a
  double-sided pointwise estimate for Lebesgue function Ln,N(x) with is depended from n
  and position of a point x on the [−1, 1] is obtained.
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 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: polynomial
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: orthogonal system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic formula
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: discrete Fourier sums
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lebesgue function
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Double-sided to Lebesgue function of Fourier sums by polynomials orthogonal on non-uniform grids
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 06-Nurmagomedov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14885/1/06-Nurmagomedov.pdf
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