Menshov representation spectra
经典分析与常微分方程
2007-05-23 v1 复变函数
摘要
A Menshov spectrum is a subset of the integers that is sufficient for representing every measurable function as an almost-everywhere converging trigonometric (non-Fourier) sum. In this language the celebrated "Menshov representation theorem" states that Z is a Menshov spectrum. In this paper we construct 1) Menshov spectra that are almost exponentially sparse 2) that are almost squares. Then we show that the positive integers are not a Menshov spectrum but are a Menshov spectrum in measure, and repeat 1) and 2) in the analytic settings.
引用
@article{arxiv.math/0510616,
title = {Menshov representation spectra},
author = {Gady Kozma and Alexander Olevskii},
journal= {arXiv preprint arXiv:math/0510616},
year = {2007}
}
备注
25 pages. Part of GK's PhD thesis