论文标题
Hardy的不确定性原理的动力版本：调查
Dynamical versions of Hardy's uncertainty principle: A survey
论文作者
论文摘要
强壮的不确定性原则表明，与高斯人相比，没有任何功能与其傅立叶变换更好地定位。该结果的教科书证明以及Hardy的原始证明之一是指phragmén-Lindelöf定理。在本说明中，我们首先描述了Hardy不确定性与Schrödinger方程的联系，并给出了基于此连接和Liouville定理的Hardy结果的新证明。证据与第二个哈迪证明有关，这已经被遗忘了。然后，我们调查了Hardy定理动态版本的最新结果。
The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. The textbook proof of the result, as well as one of the original proofs by Hardy, refers to the Phragmén-Lindelöf theorem. In this note we first describe the connection of the Hardy uncertainty to the Schrödinger equation, and give a new proof of Hardy's result which is based on this connection and the Liouville theorem. The proof is related to the second proof of Hardy, which has been underservedly forgotten. Then we survey the recent results on dynamical versions of Hardy's theorem.
