Uniform convergence criterion for non-harmonic sine series

2020/11/28 by Oganesyan, Kristina
#11L15 #40A30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.14161

Abstract

We show that for a nonnegative monotone sequence \c_k\ the condition c_kk→ 0 is sufficient for uniform convergence of the series ∑_k=1^∞c_ksin k^α x on any bounded set for α∈ (0,2), and for an odd natural α it is sufficient for uniform convergence on the whole ℝ. Moreover, the latter assertion still holds if we replace k^α by any polynomial in odd powers with rational coefficients. On the other hand, in the case of an even α it is necessary that ∑_k=1^∞c_k

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