Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces

O. L. Vinogradov, A. Yu Ulitskaya

Research output

Abstract

Let L2 be the space of 2π-periodic square-summable functions and E(f, X)2 be the best approximation of f by the space X in L2. For n ∈ ℕ and B ∈ L2, let SB , n be the space of functions s of the form s(x)=∑j=02n−1βjB(x−jπn). This paper describes all spaces SB , n that satisfy the exact inequality E(f,SB,n)2≤1nr∥f(r)∥2. (2n–1)-dimensional subspaces fulfilling the same estimate are specified. Well-known inequalities are for approximation by trigonometric polynomials and splines obtained as special cases.

Original languageEnglish
Pages (from-to)15-22
Number of pages8
JournalVestnik St. Petersburg University: Mathematics
Volume51
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

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Periodic Functions
Mean Square
Differentiable
Approximation
Estimate
Square Functions
Trigonometric Polynomial
Best Approximation
Spline
Subspace
Class

Scopus subject areas

  • Mathematics(all)

Cite this

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