University of Birmingham > Talks@bham > Analysis seminar > On Beurling's Uncertainty Principle

On Beurling's Uncertainty Principle

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Beurling showed that if f is a function on R with Fourier transform , such that ∫∫ |f(x) (y)| e|xy| dx dy is finite, then f = 0. Recently, Hedenmalm gave some information about f when ∫∫ |f(x) (y)| e|xy| dx dy = O((1 – λ) – 1) as λ → 1-. My student Xin Gao developed this to show that f is a polynomial times a Gaussian if ∫∫ |f(x) (y)| e|xy| dx dy = O((1 – λ)N) as λ → 1-. I explain his proof, and give cheap proofs of some other uncertainty principles.

This talk is part of the Analysis seminar series.

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