A continuous function with universal Fourier series on a given closed set of Lebesgue measure zero

JOURNAL OF APPROXIMATION THEORY

卷:252

Article

Khrushchev, S.¹ 

[1] Satbayev Univ, New Sch Econ, 22a Satpaev Str, Alma Ata 050013, Kazakhstan

关键词: Fourier series;    Continuous functions;    Universal Fourier series;    Convergence of Fourier series;   

DOI  :  10.1016/j.jat.2019.105361

来源: Elsevier

【 摘 要 】

Given a closed set E of Lebesgue measure zero on the unit circle T there is a continuous function f on T such that for every continuous function g on E there is a subsequence of partial Fourier sums S-n(+)(f, zeta) = Sigma(n)(k=0)(f) over cap (k)zeta(k) of f, which converges to g uniformly on E. This result completes one result in a recent paper by C. Papachristodoulos and M. Papadimitrakis (2019), see Papachristodoulos and Papadimitrakis (2019). They proved that for a classical one third Cantor set C there is no universal function in the disk algebra. They also proved that for a symmetric Cantor set C* on T there is no universal continuous function for the classical symmetric Fourier sums. See also [2]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free