论文标题
不确定性原理：主题的变化
The uncertainty principle: variations on a theme
论文作者
论文摘要
我们展示了傅立叶变换的许多众所周知的不确定性原理，例如海森伯格的不确定性原理，多诺霍（Donoho） - 坚定的不确定性原理和慕尼兰的非亚洲不确定性原理，与傅立叶变换本身的结构无关。相反，所有这些结果均来自傅立叶变换的非常弱的属性（由许多线性运算符共享），即它是作为操作员$ l^1 \ to l^\ infty $的界限，并且它是统一的。使用单个简单的证明模板，并且仅使用这些（或较弱的）属性，我们以完全统一的方式获得了这些基本不确定性原理的一些新证明和许多对这些基本不确定性原理的概括。与我们的一般概述一起，本文还可以作为对被称为不确定性原理的现象的许多方面的调查。
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.
