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arXiv · 1202.5538

Perturbing PLA

Gady Kozma·Alexander Olevskii
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Abstract

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 H\"older. We discuss also a similar problem for perturbations with lacunary spectrum.

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Gady Kozma, Alexander Olevskii. 2012-02-24. Perturbing PLA. https://arxiv.org/abs/1202.5538

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