Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $ {H_{{\omega_p}}} $ in the metrics of the spaces L p

Autor:	I. V. Sokolenko, A. S. Serdyuk
Rok vydání:	2010
Předmět:	Polynomial (hyperelastic model) Combinatorics symbols.namesake Approximations of π General Mathematics Metric (mathematics) symbols Linear approximation Space (mathematics) Poisson distribution Linear methods Omega Mathematics
Zdroj:	Ukrainian Mathematical Journal. 62:1139-1157
ISSN:	1573-9376 0041-5995
DOI:	10.1007/s11253-010-0419-2
Popis:	We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from $ {H_{{\omega_p}}} $ for 1 ≤ p < ∞ by a certain linear method U n * in the metric of the space L p . It is shown that the obtained estimates are asymptotically exact for p = 1: In addition, we determine the asymptotic equalities for the best approximations of the classes of Poisson integrals of functions from $ {H_{{\omega_1}}} $ in the metric of the space L 1 and show that, for these classes, the method U n * is the best polynomial approximation method in a sense of strong asymptotic behavior.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1f27532978d9caf8d34b701950666bec https://doi.org/10.1007/s11253-010-0419-2 Zobrazit plný text záznamu Plný text ve formátu PDF