Gabor duality theory for Morita equivalent C∗-algebras
Gabor duality theory for Morita equivalent C∗-algebras
复制标题
Morita 等价 C*-代数的 Gabor 对偶理论
DOI：
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发表时间：
2019
影响因子：
0.6
通讯作者：
F. Luef
中科院分区：
文献类型：
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作者：
A. Austad;Mads S. Jakobsen;F. Luef
Gabor框架的对偶原理是Gabor分析的支柱之一。我们建立了具有一些额外性质的Morita等价双模的一个深远的推广。对于某些扭群[公式：见正文]-代数，通过关于迹的局部化，将对偶原理重新表述为Morita等价双模的设置，从而简化为著名的Gabor对偶原理。我们可以将模级上的所有结果提升到矩阵代数和矩阵模上，在这样做的过程中，自然会引入[公式：参见正文]-矩阵Gabor框架，它推广了多窗口超级Gabor框架。我们还能够建立等价双模上的模框架的密度定理，并且这些定理局部化为[公式：见正文]-矩阵Gabor框架的密度定理。
The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalence bimodules with some extra properties. For certain twisted group [Formula: see text]-algebras, the reformulation of the duality principle to the setting of Morita equivalence bimodules reduces to the well-known Gabor duality principle by localizing with respect to a trace. We may lift all results at the module level to matrix algebras and matrix modules, and in doing so, it is natural to introduce [Formula: see text]-matrix Gabor frames, which generalize multi-window super Gabor frames. We are also able to establish density theorems for module frames on equivalence bimodules, and these localize to density theorems for [Formula: see text]-matrix Gabor frames.