Stability of shifts, interpolation, and crystalline measures

Abstract

Let $V_{\Gamma }^p(\mathcal{G}),1\le p\le \infty ,$ be the quasi shift-invariant space generated by $\Gamma$-shifts of a function $\mathcal{G}$, where $\Gamma \subset \mathbb{R}$ is a separated set. For several large families of generators $\mathcal{G}$, we present necessary and sufficient conditions on $\Gamma$ that imply that the $\Gamma$-shifts of $\mathcal{G}$ form an unconditional basis for $V_{\Gamma }^p(\mathcal{G})$. The connection between this property, interpolation, universal interpolation, and crystalline measures is discussed.

23 pages

References in corpus (3)

• Stable polynomials and crystalline measures
• Sampling in the shift-invariant space generated by the bivariate Gaussian function
• Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials