Everywhere divergent trigonometric series
Abstract
This paper establishes the existence of everywhere divergent trigonometric series with various kinds of gaps. It is shown, for example, that for every positive integer$\lambda$there are$r_n\to0$and$\gamma_n$such that $\sum_{n=1}^\infty r_n\cos(n^\lambda x-\gamma_n+\varphi)$ diverges tor all$x$and$\varphi$in$(-\infty,+\infty)$.Bibliography: 7 titles.
Submission history
[v1] 1971