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arXiv · 2410.08682

Stability of shifts, interpolation, and crystalline measures

Alexander Ulanovskii·Ilya Zlotnikov
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Abstract

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.

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Alexander Ulanovskii, Ilya Zlotnikov. 2024-11-23. Stability of shifts, interpolation, and crystalline measures. https://doi.org/10.1112/jlms.70267

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