不确定性原理：主题的变化
The uncertainty principle: variations on a theme
摘要：
我们展示了如何一些著名的不确定性原则的傅里叶变换，如海森堡不确定性原则，多诺霍-斯塔克不确定性原则，和Meshulam的非阿贝尔不确定性原则，有一点关系的傅里叶变换本身的结构。相反，所有这些结果都来自傅里叶变换的非常弱的性质（由许多线性算子共享），即它作为算子$L^1 \to L^\infty$是有界的，并且它是酉的。使用一个单一的，简单的证明模板，只有这些（或较弱的）性质，我们获得了一些新的证明和这些基本的不确定性原则的许多推广，新的运营商和新的设置，在一个完全统一的方式。连同我们的一般概述，本文也可以作为一个调查的许多方面的现象称为不确定性原则。
英文摘要：
We show how a number of well-known uncertainty principles for the Fourier transform, such as the Heisenberg uncertainty principle, the Donoho--Stark uncertainty principle, and Meshulam's non-abelian uncertainty principle, have little to do with the structure of the Fourier transform itself. Rather, all of these results follow from very weak properties of the Fourier transform (shared by numerous linear operators), namely that it is bounded as an operator $L^1 \to L^\infty$, and that it is unitary. Using a single, simple proof template, and only these (or weaker) properties, we obtain some new proofs and many generalizations of these basic uncertainty principles, to new operators and to new settings, in a completely unified way. Together with our general overview, this paper can also serve as a survey of the many facets of the phenomena known as uncertainty principles.
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。
