A note on approximation by trigonometric polynomials

Результат исследований: Научные публикации в периодических изданияхстатья


Let E=∪k=1n[akbk]⊂ℝ; if n > 1, then we assume that the segments [a k, b k] are pairwise disjoint. Assume that the following property holds: E ∩ (E + 2πν) = ∅, ν ∈ ℤ, ν ≠ 0. Denote by H ω + r(E) the space of functions f defined on E such that |f (r)(x 2) − f (r)(x 1)| ≤ c fω(|x 2 − x 1|), x 1, x 2 ∈ E, f (0) ≡ f. Assume that a modulus of continuity ω satisfies the condition∫0xω(t)tdt+x∫x∞ω(t)t2dt≤cω(x). We find a constructive description of the space H ω + r(E) in terms of the rate of nonuniform approximation of a function f ∈ H ω + r(E) by trigonometric polynomials if E and ω satisfy the above conditions.

Язык оригиналаанглийский
Страницы (с-по)981-984
ЖурналJournal of Mathematical Sciences
Номер выпуска6
СостояниеОпубликовано - 2019


Предметные области Scopus

  • Математика (все)