TY - JOUR

T1 - A note on approximation by trigonometric polynomials

AU - Shirokov, N. A.

N1 - Shirokov, N.A. A Note on Approximation by Trigonometric Polynomials. J Math Sci 243, 981–984 (2019) doi:10.1007/s10958-019-04598-y

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85075342809&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04598-y

DO - 10.1007/s10958-019-04598-y

M3 - Article

VL - 243

SP - 981

EP - 984

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -