Discrete Translates in Lp (R)

Abstract

A set $\Lambda$ is called $p$-spectral if there is a function $g \in L^p (\mathbb{R})$ such that all $\Lambda$-translates $\{g(t-\lambda),\lambda \in \Lambda\}$ span $L^p(\mathbb{R})$. We prove that exponentially small non-zero pertubations of the integers are p-spectral for all $p>1$.