Perturbing PLA

Gady Kozma*, Alexander Olevskii

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)279-298
Number of pages20
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - Oct 2013


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