A Sharp Jackson–Chernykh Type Inequality for Spline Approximations on the Line

Research output

Abstract

An analog of the Jackson–Chernykh inequality for spline approximations in the space L2( ℝ) is established in this work. For r ℕ and σ > 0, we denote by Aσr( f )2 the best approximation of a function f ∈ L2(ℝ ) by the space of splines of degree r of minimal defect with knots , j ∏/σ , and by ω( f, δ)2 the first-order modulus of continuity of f in L2( ℝ). The main result of our work is as follows. For any f ∈ L2( ℝ),(formula presented) where θr = 1/√1-εr 2 and εr is the positive root of the equation(formula presented) The constant 1/√2 cannot be reduced on the whole class L2(ℝ ) even by increasing the step of the modulus of continuity.

Original languageEnglish
Pages (from-to)10-19
Number of pages10
JournalVestnik St. Petersburg University: Mathematics
Volume53
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020

Scopus subject areas

  • Mathematics(all)

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