A generalization of the Beurling-Hedenmalm uncertainty principle

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Copyright: Gao, Xin
Abstract
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.
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Author(s)
Gao, Xin
Supervisor(s)
Michael, Cowling
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Publication Year
2016
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Thesis
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PhD Doctorate
UNSW Faculty
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