# Sergey Favorov: Measures and temperate distributions with discrete support and spectrum

**Time: **
Wed 2022-04-27 13.15 - 14.15

**Location: **
Kräftriket, House 6, Room 306 and Zoom

**Video link: **
Meeting ID: 692 1892 7142

**Participating: **
Sergey Favorov (Kharkiv National University)

### Abstract

Consider a measure on Euclidean space with discrete support such that its distributional Fourier transform also a measure with discrete support (so called crystalline measure). We investigate conditions for support of the measure to be a finite union of translated full-rank lattices and give a complete description of such measures. The proof is based on Cohen's Idempotent Theorem and a new local analog of Wiener's Theorem on trigonometric series. Also we show generalizations of these results to temperate distributions with discrete support. Moreover, as application of above results we find a new sufficient condition for a discrete set in Euclidean space to be a coherent set of frequencies.