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<p>In this article, we introduce and investigate Hilbert-Schmidt Gabor-like frames on an LCA group with time-frequency shifts along a closed subgroup of the phase space. We first prove a density theorem which says that for such a frame, the index subgroup is necessarily co-compact. Moreover, an inequality about the density of this subgroup, the operator norm of the generator and frame bounds is established. Then we provide some properties of such frames by using this density theorem. Finally, dual Hilbert-Schmidt Gabor-like frames are characterized and Riesz properties of such frames are obtained. Our work is original even in the Euclidean case.</p>

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Hilbert-Schmidt Gabor-Like Frames on LCA Groups

  • 期刊论文

  • 发表日期：

    2025年1月11日

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  • Pengtong Li,
  • Jingsheng Wang

摘要

In this article, we introduce and investigate Hilbert-Schmidt Gabor-like frames on an LCA group with time-frequency shifts along a closed subgroup of the phase space. We first prove a density theorem which says that for such a frame, the index subgroup is necessarily co-compact. Moreover, an inequality about the density of this subgroup, the operator norm of the generator and frame bounds is established. Then we provide some properties of such frames by using this density theorem. Finally, dual Hilbert-Schmidt Gabor-like frames are characterized and Riesz properties of such frames are obtained. Our work is original even in the Euclidean case.