论文标题
广义标志傅里叶不确定性
Generalized sign Fourier uncertainty
论文作者
论文摘要
我们考虑了傅立叶变换的标志不确定性原理的广义版本，首先由Bourgain，Clozel和Kahane于2010年提出，并在2019年由Cohn和Gonçalves重新审视。在我们的设置中，功能的迹象及其傅立叶变换的符号以一般的给定功能$ p $在球外的函数上共鸣。本质上，一个人想知道这种共鸣是否会在面对合适的加权积分状态时是否会发生。该问题的原始版本对应于情况$ p \ equiv 1 $。令人惊讶的是，即使在如此粗糙的设置中，我们在某些情况下也能够识别出锋利的常数。
We consider a generalized version of the sign uncertainty principle for the Fourier transform, first proposed by Bourgain, Clozel and Kahane in 2010 and revisited by Cohn and Gonçalves in 2019. In our setup, the signs of a function and its Fourier transform resonate with a generic given function $P$ outside of a ball. One essentially wants to know if and how soon this resonance can happen, when facing a suitable competing weighted integral condition. The original version of the problem corresponds to the case $P \equiv 1$. Surprisingly, even in such a rough setup, we are able to identify sharp constants in some cases.
