Séminaire Analyse Harmonique
Density criteria for Fourier uniqueness phenomena in $\mathbb{R}^d$
07
Oct. 2024
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Intervenant : Anshul Adve
Institution : Princeton University
Heure : 14h00 - 15h00
Lieu : Bâtiment 307, salle 3L15

A remarkable byproduct of the work of Viazovska et al. on sphere packing is the notion of a "Fourier uniqueness set": a discrete subset $A$ of $\mathbb{R}^d$ such that any Schwarz function on $\mathbb{R}^d$ is determined by its restriction and the restriction of its Fourier transform to $A$. Once one knows such sets exist, it is natural to ask how dense they must be / how sparse they can be. This was determined in dimension 1 by Kulikov, Nazarov, and Sodin, but the higher dimensional story was much less well understood. We will give an answer in all dimensions using new methods.

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