Discrete Translates in Function Spaces

Abstract

We construct a Schwartz function $\phi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\phi (t-\lambda ),\lambda \in \Lambda \}$ spans the space $L^p(R)$, for every $p>1$. This result remains true for more general function spaces $X$, whose norm is "weaker" than $L^1$ (on bounded functions).

References in corpus (2)

• Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon
• Completeness in $L^1(R)$ of discrete translates

Cited by in corpus (1)

• Completeness of Discrete Translates in $H^1(\mathbb{R})$