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On Beurling's Uncertainty PrincipleAdd to your list(s) Download to your calendar using vCal
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:Note that ex-directory lists are not shown. |
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