# Fourier uniqueness pairs of powers of integers

### João P. G. Ramos

ETH Zürich, Switzerland### Mateus Sousa

Ludwig-Maximilians Universität München, Germany

## Abstract

We prove, under certain conditions on ${(\alpha,\beta)}$, that each Schwartz function ${f}$ such that ${f(\pm n^{\alpha}) = \widehat{f}(\pm n^{\beta}) = 0}$ for all ${n \ge 0}$ must vanish identically, complementing a series of recent results involving uncertainty principles, such as the pointwise interpolation formulas by Radchenko and Viazovska and the Meyer–Guinnand construction of self-dual crystaline measures.

## Cite this article

João P. G. Ramos, Mateus Sousa, Fourier uniqueness pairs of powers of integers. J. Eur. Math. Soc. 24 (2022), no. 12, pp. 4327–4351

DOI 10.4171/JEMS/1194