Trigonometric series with noninteger harmonics

被引：2

作者：

Gabdullin, Mikhail R. ^{[1
]}

机构：

[1] Steklov Math Inst, Gubkina str, 8, Moscow 119991, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 508卷 / 01期

关键词：

Trigonometric series; Uniform convergence; Exponential sums; UNIFORM-CONVERGENCE;

D O I：

10.1016/j.jmaa.2021.125792

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let {c(k)} be a nonincreasing sequence of positive numbers (more general classes of sequences are also considered), and alpha > 0 be not an integer. We find necessary and sufficient conditions for the uniform convergence of the series Sigma(k) c(k) sin k(alpha)x and Sigma(k) c(k) cos k(alpha)x on the real line and its bounded subsets. (c) 2021 Published by Elsevier Inc.

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