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Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces. / Vinogradov, O. L.; Ulitskaya, A. Yu.

в: Vestnik St. Petersburg University: Mathematics, Том 51, № 1, 01.01.2018, стр. 15-22.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Vinogradov, OL & Ulitskaya, AY 2018, 'Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces', Vestnik St. Petersburg University: Mathematics, Том. 51, № 1, стр. 15-22. https://doi.org/10.3103/S1063454118010120

APA

Vinogradov, O. L., & Ulitskaya, A. Y. (2018). Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces. Vestnik St. Petersburg University: Mathematics, 51(1), 15-22. https://doi.org/10.3103/S1063454118010120

Vancouver

Vinogradov OL, Ulitskaya AY. Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces. Vestnik St. Petersburg University: Mathematics. 2018 Янв. 1;51(1):15-22. https://doi.org/10.3103/S1063454118010120

Author

Vinogradov, O. L. ; Ulitskaya, A. Yu. / Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces. в: Vestnik St. Petersburg University: Mathematics. 2018 ; Том 51, № 1. стр. 15-22.

BibTeX

@article{794702fc4eb24814b5cb88a59a5f26f2,
title = "Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces",
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.",
keywords = "best approximation, sharp constants, shift spaces",
author = "Vinogradov, {O. L.} and Ulitskaya, {A. Yu}",
year = "2018",
month = jan,
day = "1",
doi = "10.3103/S1063454118010120",
language = "English",
volume = "51",
pages = "15--22",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces

AU - Vinogradov, O. L.

AU - Ulitskaya, A. Yu

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - best approximation

KW - sharp constants

KW - shift spaces

UR - http://www.scopus.com/inward/record.url?scp=85045068984&partnerID=8YFLogxK

U2 - 10.3103/S1063454118010120

DO - 10.3103/S1063454118010120

M3 - Article

AN - SCOPUS:85045068984

VL - 51

SP - 15

EP - 22

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 37832541