We refine a result of Matei and Meyer on stable sampling and stable interpolation for simple model sets. Our setting is model sets in locally compact abelian groups and Fourier analysis of unbounded complex Radon measures as developed by Argabright and de Lamadrid. This leads to a refined version of the underlying model set duality between sampling and interpolation. For rather general model sets, our methods also yield an elementary proof of stable sampling and stable interpolation sufficiently far away from the critical density, which is based on the Poisson Summation Formula.

中文翻译：

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通过模型集进行采样和插值

我们对简单模型集的稳定采样和稳定插值改进了Matei和Meyer的结果。我们的设置是局部紧凑的阿贝尔群中的模型集，以及由Argabright和de Lamadrid开发的无界复杂Radon量度的傅立叶分析。这导致采样和插值之间基础模型集对偶性的改进版本。对于相当普通的模型集，我们的方法还基于Poisson求和公式，提供了足以远离临界密度的稳定采样和稳定插值的基本证明。