令人不安的PLA
Perturbing PLA
摘要：
我们在前面证明了，圆上的每个可测函数，在一个均匀的小扰动之后，都可以写成一个幂级数（即一系列具有正频率的指数），它几乎处处收敛。在这里，我们表明，这个结果基本上是尖锐的：扰动不能光滑，甚至霍德尔。我们还讨论了缺谱扰动的一个类似问题。
英文摘要：
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 discuss also a similar problem for perturbations with lacunary spectrum.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
