框架势与有限阿贝尔群
Frame potential and finite abelian groups
摘要：
本文继续了作者先前的研究，目的是将卷积紧框架的特征结果从循环群的背景扩展到一般的有限阿贝尔群。研究的集合是由一个固定的子群的元素，并通过翻译一些\emph{generators}，它示出，在一定的规范条件下，这种结构的紧框架的特点是局部极小的框架潜力。对有限阿贝尔群的任意子群，研究了有限循环群的下采样和上采样算子的自然类似物。并提出了进一步研究的方向。
英文摘要：
This article continues a prior investigation of the authors with the goal of extending characterization results of convolutional tight frames from the context of cyclic groups to general finite abelian groups. The collections studied are formed by translating a number of \emph{generators} by elements of a fixed subgroup and it is shown, under certain norm conditions, that tight frames with this structure are characterized as local minimizers of the frame potential. Natural analogs to the downsampling and upsampling operators of finite cyclic groups are studied for arbitrary subgroups of finite abelian groups. Directions of further study are also proposed.
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