Ullrich, Grubb and Moore proved that a lacunary trigonometric series satisfying Hadamard's gap condition is recurrent a.e. We prove the existence of a recurrent trigonometric series with bounded gaps.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-2-10,
author = {Katusi Fukuyama and Dinesh Neupane},
title = {Recurrence for cosine series with bounded gaps},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {281-284},
zbl = {1206.42005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-2-10}
}
Katusi Fukuyama; Dinesh Neupane. Recurrence for cosine series with bounded gaps. Colloquium Mathematicae, Tome 120 (2010) pp. 281-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-2-10/