# Large Fourier Quasicrystals and Wiener's Theorem

## TL;DR

This paper introduces new conditions for when a discrete measure's support is a finite union of translated lattices, using Wiener's Theorem and almost periodic functions to advance mathematical understanding.

## Contribution

It provides novel simple criteria linking measure support structures to harmonic analysis tools like Wiener's Theorem.

## Key findings

- Support of discrete measures characterized as finite unions of translated lattices.
- New conditions derived from Wiener's Theorem and almost periodic functions.
- Enhanced understanding of measure support structures in Euclidean space.

## Abstract

We find new simple conditions for support of a discrete measure on Euclidean space to be a finite union of translated lattices. The arguments are based on a local analog of Wiener's Theorem on absolutely convergent trigonometric series and theory of almost periodic functions.