Fourier uniqueness in $\mathbb{R}^4$
Andrew Bakan, Haakan Hedenmalm, Alfonso Montes-Rodriguez, Danylo, Radchenko, Maryna Viazovska
TL;DR
This paper explores the connection between Fourier interpolation uniqueness in four-dimensional space and Heisenberg uniqueness for the Klein-Gordon equation, revealing a known interrelation since 2017.
Contribution
It establishes a link between Fourier interpolation uniqueness and Heisenberg uniqueness for Klein-Gordon, building on prior knowledge from 2017.
Findings
Identifies the interrelation between Fourier interpolation and Heisenberg uniqueness.
Connects recent Fourier interpolation formulas with classical Heisenberg problems.
Builds on known results from 2017 to deepen understanding of Fourier uniqueness.
Abstract
We show an interrelation between the uniqueness aspect of the recent Fourier interpolation formula of Radchenko and Viazovska and the Heisenberg uniqueness study for the Klein-Gordon equation and the lattice-cross of critical density, studied by Hedenmalm and Montes-Rodriguez. This has been known since 2017.
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Taxonomy
TopicsStochastic processes and financial applications