$L^2（\mathbb｛R｝^｛2N｝）中的扭转平移不变系统$

Pub Date : 2023-06-05 DOI:10.1017/nmj.2023.11

Santi Ranjan Das, R. Velsamy, Radha Ramakrishnan

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引用次数: 0

摘要

摘要我们考虑了一个由可数多个生成元的扭曲平移组成的一般扭曲移位不变系统$V^｛t｝（\mathcal｛a｝）$，并研究了获得系统$V^{t｝的特征以形成帧序列或Riesz序列的问题。我们用一些例子来说明我们的理论。除这些结果外，我们还研究了一个双扭移不变量系统，并从给定的扭平移序列Riesz中得到了一个扭平移的正交序列。

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TWISTED SHIFT-INVARIANT SYSTEM IN $L^2(\mathbb {R}^{2N})$

Abstract 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.

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