We consider a general twisted shift-invariant system, $V^{t}(\mathcal {A})$, consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system $V^{t}(\mathcal {A})$ to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.

中文翻译：

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扭曲平移不变系统

我们考虑一个通用的扭曲平移不变系统$V^{t}(\mathcal {A})$ ，由可数个生成器的扭曲平移组成，并研究获得系统$V^{t}表征的问题(\mathcal {A})$形成帧序列或 Riesz 序列。我们用一些例子来说明我们的理论。除了这些结果之外，我们还研究了双扭曲平移不变系统，并从给定的扭曲平移序列中获得了正交的扭曲平移序列。