DYNAMICAL VERSIONS OF HARDY'S UNCERTAINTY PRINCIPLE: A SURVEY

被引：11

作者：

Fernandez-Bertolin, Aingeru ^{[1
]}

Malinnikova, Eugenia ^{[2
,3
]}

机构：

[1] Univ Basque Country, Euskal Herriko Unibertsitatea, UPV EHU, Dept Matemat, Apartado 644, E-48080 Bilbao 48080, Spain

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[3] Norwegian Univ Sci & Technol, Dept Math Sci, Trondheim, Norway

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 58卷 / 03期

基金：

欧洲研究理事会;

关键词：

Uncertainty principle; Schrodinger equation; UNIQUENESS PROPERTIES; CONVEXITY;

D O I：

10.1090/bull/1729

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Phragmen-Lindelof theorem. In this note we first describe the connection of the Hardy uncertainty to the Schrodinger 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 undeservedly forgotten. Then we survey the recent results on dynamical versions of Hardy's theorem.

引用

页码：357 / 375

页数：19

共 43 条

[1]

Agmon S., SEM MATH SUP

[2] UNCERTAINTY PRINCIPLE FOR DISCRETE SCHRODINGER EVOLUTION ON GRAPHS [J].