naa a22 4500 510781365 CHVBK 20180411083248.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11854-013-0036-8 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0036-8 Perturbing PLA [Elektronische Daten] [Gady Kozma, Alexander Olevskii] We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e., a series of exponentials with positive frequencies), which converges almost everywhere. Here, we show that this result is basically sharp: the perturbation cannot be made smooth or even Hölder. We also discuss a similar problem for perturbations with lacunary spectrum. Hebrew University Magnes Press, 2013 Kozma Gady Department of Mathematics, Weizmann Institute of Science, 7619991, Rehovot, Israel aut Olevskii Alexander School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 279-298 0021-7670 121:1<279 2013 121 11854 https://doi.org/10.1007/s11854-013-0036-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0036-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kozma Gady Department of Mathematics, Weizmann Institute of Science, 7619991, Rehovot, Israel aut NATIONALLICENCE 700 1- Olevskii Alexander School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 279-298 0021-7670 121:1<279 2013 121 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer