Sharp estimates of approximation of periodic functions in Hölder spaces

Yurii Kolomoitsev; Jürgen Prestin

doi:10.1016/j.jat.2015.07.004

Sharp estimates of approximation of periodic functions in Hölder spaces

Yurii Kolomoitsev^*, Jürgen Prestin

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Mathematik

5 Zitate (Scopus)

Abstract

The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the Hölder spaces H_p^r,α for all 0 < p≤ ∞ and 0 < α ≤ r. By using modifications of the classical moduli of smoothness, we give improvements of the direct and inverse theorems of approximation and prove the criteria for the precise order of decrease of the best approximation in these spaces. Moreover, we obtained strong converse inequalities for general methods of approximation of periodic functions in H_p^r,α.

Originalsprache	Englisch
Zeitschrift	Journal of Approximation Theory
Jahrgang	200
Seiten (von - bis)	68-91
Seitenumfang	24
ISSN	0021-9045
DOIs	https://doi.org/10.1016/j.jat.2015.07.004
Publikationsstatus	Veröffentlicht - 01.12.2015

Fördermittel

The authors are indebted to the referees for a thorough reading and valuable suggestions, which allowed them to improve this paper considerably. The authors were supported by FP7-People-2011-IRSES Project number 295164 (EUMLS: EU-Ukrainian Mathematicians for Life Sciences). The first author was supported by the Grant of the National Academy of Sciences of Ukraine for young scientists.

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AB - The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the Hölder spaces Hpr,α for all 0 < p≤ ∞ and 0 < α ≤ r. By using modifications of the classical moduli of smoothness, we give improvements of the direct and inverse theorems of approximation and prove the criteria for the precise order of decrease of the best approximation in these spaces. Moreover, we obtained strong converse inequalities for general methods of approximation of periodic functions in Hpr,α.

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Sharp estimates of approximation of periodic functions in Hölder spaces

Abstract

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