Perturbing PLA
Classical Analysis and ODEs
2012-02-27 v1
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.
Keywords
Cite
@article{arxiv.1202.5538,
title = {Perturbing PLA},
author = {Gady Kozma and Alexander Olevskii},
journal= {arXiv preprint arXiv:1202.5538},
year = {2012}
}
Comments
21 pages