Stability of shifts, interpolation, and crystalline measures

2024/10/11 by Alexander Ulanovskii, Ulanovskii, Alexander, Ilya Zlotnikov +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.08682

Abstract

Let V^p_Γ(G),1≤ p≤∞, be the quasi shift-invariant space generated by Γ-shifts of a function G, where Γ⊂ℝ is a separated set. For several large families of generators G, we present necessary and sufficient conditions on Γ that imply that the Γ-shifts of G form an unconditional basis for V^p_Γ(G). The connection between this property, interpolation, universal interpolation, and crystalline measures is discussed.

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