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 $(-\infty,+\infty)$.
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