title: Sharp Jackson - Chernykh type inequality for spline approximations on the line
metadata.name: dc.contributor.author
metadata.value: Vinogradov, Oleg L.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:17:09Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:17:09Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vinogradov O. L. Sharp Jackson - Chernykh type inequality for spline approximations on the line. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 15–27.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.102
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17324
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: An analog of the Jackson Chernykh inequality for spline approximations in the space
  L2(R) is established. For r 2 N, σ > 0, we denote by A r(f)2 the best approximation of
  a function f 2 L2(R) by the space of splines of degree r and of minimal defect with knots
  j 
    , j 2 Z, and by ω(f, δ) its first order modulus of continuity in L2(R). The main result of
  the paper is the following. For every f 2 L2(R)
  A r(f)2 6
  1
  p2
  ω  f,
  θrπ
  σ  2
  ,
  where εr is the positive root of the equation
  4ε2(ch  "
    − 1)
  ch  "
    + cos  
   
  =
  1
  32r−2
  , τ = p1 − ε2,
  θr = 1 p1−"2
  r
  . The constant 1 p2
  cannot be reduced on the whole class L2(R), even if one
  insreases the step of the modulus of continuity.
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 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: Jackson inequality
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: splines
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: sharp constants
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Sharp Jackson - Chernykh type inequality for spline approximations on the line
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15-27.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17324/1/15-27.pdf
resources.format: Adobe PDF
resources.size: 342,54 kB