Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts

Research output

Abstract

Let σ > 0, and let G,B ∈ L(ℝ). This paper is devoted to approximation of convolution classes f = ϕ*G, ϕ ∈ Lp(ℝ), by a space SB that consists of functions of the form. Under some conditions on G and B, linear operators Xσ,G,B with values in SB are constructed for which ||f -Xσ,G,B(f)||p ≤ Kσ,G||ϕ||p. For p = 1,∞ the constant Kσ,G (it is an analog of the well-known Favard constant) cannot be reduced, even if one replaces the left-hand side by the best approximation by the space SB. The results of the paper generalize classical inequalities for approximations by entire functions of exponential type and by splines.

Original languageEnglish
Pages (from-to)841-867
Number of pages27
JournalSt. Petersburg Mathematical Journal
Volume30
Issue number5
DOIs
Publication statusPublished - 1 Jan 2019

Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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