Trigonometric series with noninteger harmonics

2021/02/10 by Gabdullin, Mikhail R.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.05698

Abstract

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 ∑_k c_ksin k^αx and ∑_k c_kcos k^αx on the real line and its bounded subsets.

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