English

Trigonometric series with noninteger harmonics

Classical Analysis and ODEs 2021-12-07 v3

Abstract

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

Cite

@article{arxiv.2102.05698,
  title  = {Trigonometric series with noninteger harmonics},
  author = {Mikhail R. Gabdullin},
  journal= {arXiv preprint arXiv:2102.05698},
  year   = {2021}
}
R2 v1 2026-06-23T23:03:00.670Z