Naser Sardari

Higher Fourier interpolation on the plane

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 { √|n| : n \in \mathbb{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.