arXiv 2102.056982021-02math.CA

Trigonometric series with noninteger harmonics

Mikhail R. Gabdullin

英文摘要：

Let $\{c_k\}$ be a nonincreasing sequence of positive numbers (more general classes of sequences are also considered), and $α>0$ be not an integer. We find necessary and sufficient conditions for the uniform convergence of the series $\sum_k c_k\sin k^αx$ and $\sum_k c_k\cos k^αx$ on the real line and its bounded subsets.

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