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/