A generalization of the Beurling-Hedenmalm uncertainty principle

We study the uncertainty principles of Hardy and of Beurling, and functions that "only just" satisfy the inequalities of uncertainty principles. More specifically, we show that if a function and its Fourier transform have nearly gaussian decay, the the coefficients of its Hermite expansion decay fast, and vice versa. We give a new and simple proof of generalisation of Beurling's uncertainty principle first in R using complex analysis. Then we generalise to R^n using various techniques. Also we illustrate connections with the classical moment problem.

Grantor dc:publisher

UNSW, Sydney

Year dc:date

2016

Author dc:creator

• Gao, Xin

• Complex analysis
• Uncertainty principle
• Harmonic analysis

Statement dc:rights

• open access
• CC BY-NC-ND 3.0
• free_to_read

Licence

• https://purl.org/coar/access_right/c_abf2
• https://creativecommons.org/licenses/by-nc-nd/3.0/au/

Language dc:language

EN

Identifier

https://doi.org/10.26190/unsworks/19044

OAI identifier oai:identifier

oai:unsworks.library.unsw.edu.au:1959.4/56312