On Beurling's Uncertainty Principle

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• Michael Cowling (University of New South Wales, Australia)
• Tuesday 05 May 2015, 16:00-17:00
• Lecture Theatre 3, Strathcona Building.

If you have a question about this talk, please contact Alessio Martini.

Beurling showed that if f is a function on R with Fourier transform fˆ, such that ∫∫ |f(x) fˆ(y)| e^|xy| dx dy is finite, then f = 0. Recently, Hedenmalm gave some information about f when ∫∫ |f(x) fˆ(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) fˆ(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.

This talk is included in these lists:

• Analysis seminar
• Lecture Theatre 3, Strathcona Building
• School of Mathematics events

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