Let σ > 0, m, r ∈ ℕ, m ≥ r, let Sσ,m be the space of splines of order m and minimal defect with nodes jπσ (j ∈ ℤ), and let Aσ,m(f)p be the best approximation of a function f by the set Sσ,m in the space Lp(ℝ). It is known that for p = 1,+∞, (Formula presented.) where Kr are the Favard constants. In this paper, linear operators Xσ,r,m with values in Sσ,m such that for all p ∈ [1,+∞] and f ∈ Wp (r)(ℝ),ǁf−Xσ,r,m(f)ǁp≤Krrǁf(r)ǁp are constructed. This proves that the upper bounds indicated above can be achieved by linear methods of approximation, which was previously unknown. Bibliography: 21 titles.

Original languageEnglish
Pages (from-to)3-22
Number of pages20
JournalJournal of Mathematical Sciences (United States)
Volume217
Issue number1
Early online date7 Jul 2016
DOIs
StatePublished - 1 Aug 2016

    Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

ID: 15680306