Stability of shifts, interpolation, and crystalline measures
Alexander Ulanovskii, Ilya Zlotnikov · arXiv (Cornell University) · 2024
Let $V^p_Γ(\mathcal{G}),1\leq p\leq\infty,$ be the quasi shift-invariant space generated by $Γ$-shifts of a function $\mathcal{G}$, where $Γ\subset\mathbb{R}$ is a separated set. For several large families of generators $\mathcal{G}$, we present necessary and sufficient conditions on $Γ$ that imply that the $Γ$-shifts of $\mathcal{G}$ form an unconditional basis for $V^p_Γ(\mathcal{G})$. The connection between this property, interpolation, universal interpolation, and crystalline measures is discussed.