Higher Fourier interpolation on the plane

Abstract: Radchenko and Viazovska recently proved an elegant formula that expresses the value of the Schwartz function $f$ at any given point in terms of the values of $f$ and its Fourier transform on the set $\{ \sqrt{|n|}:n\in \Z\}.$ We develop new interpolation formulas using the values of the higher derivatives on new discrete sets.

In particular, we prove a conjecture of Cohn, Kumar, Miller, Radchenko and Viazovska that was motivated by the universal optimality of the hexagonal lattice.

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

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