We study spanning properties of a family of functions translated along simple model sets. We characterize tight frame and dual frame generators for such irregular translates and we apply the results to Gabor systems. We use the connection between model sets and almost periodic functions and rely strongly on a Poisson summations formula for model sets to introduce the so-called bracket product, which then plays a crucial role in our approach. As a corollary to our main results we obtain a density statement for semi-regular Gabor frames.

中文翻译：

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模型集的翻译帧

我们研究沿简单模型集转换的一系列函数的跨越特性。我们描述了这种不规则平移的紧框架和双框架生成器，并将结果应用于 Gabor 系统。我们使用模型集和几乎周期函数之间的联系，并强烈依赖模型集的泊松求和公式来引入所谓的括号乘积，这在我们的方法中起着至关重要的作用。作为我们主要结果的推论，我们获得了半规则 Gabor 框架的密度陈述。