# Yves Meyer: Spikes and waves

Mikael Passare Day

**Time: **
Wed 2021-09-15 14.15 - 15.00

**Location: **
Stockholm University, Kräftriket, Room 14 and Zoom 694 2604 1151

**Participating: **
Yves Meyer (Ecole Normale Supérieure de Cachan)

### Abstract

An atomic measure on \(\mathbb{R}^n\) is a crystalline measure if it is supported by a locally finite set and if its distributional Fourier transform is also supported by a locally finite set. Crystalline measures were introduced in 1959 by Andrew Guinand, Jean-Pierre Kahane, and Szolem Mandelbrojt. Recent results show that crystalline measures play a seminal role in the following problem on Schwartz functions. One is given two locally finite sets *E* and *F*. We demand that the only Schwartz function *f* vanishing on *E* and whose Fourier transform vanishes on *F* be the zero function. Finally this investigation applies to the solution by Maryna Viazovska of the packing Kepler problem in dimension 8.