Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity

Autor:	I. V. Sokolenko, A. S. Serdyuk
Rok vydání:	2016
Předmět:	Sequence General Mathematics 010102 general mathematics Mathematical analysis Zero (complex analysis) 010103 numerical & computational mathematics Space (mathematics) 01 natural sciences Modulus of continuity Moduli Periodic function Metric (mathematics) 0101 mathematics Fourier series Mathematics
Zdroj:	Mathematical Notes. 99:901-915
ISSN:	1573-8876 0001-4346
DOI:	10.1134/s0001434616050291
Popis:	We obtain asymptotic estimates for best approximations by trigonometric polynomials in the metric of the space C(Lp) for classes of periodic functions expressible as convolutions of kernels Ψβ with Fourier coefficients decreasing to zero faster than any power sequence, and with functions ϕ ∈ C (ϕ ∈ Lp) whose moduli of continuity do not exceed the given majorant of ω(t). It is proved that, in the spaces C and L1, for convex moduli of continuity ω(t), the obtained estimates are asymptotically sharp.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9b82dec5f3602e88765156a0f0c322ed https://doi.org/10.1134/s0001434616050291 Zobrazit plný text záznamu Plný text ve formátu PDF