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Gabor duality theory for Morita equivalent C∗-algebras
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2020-05-20 , DOI: 10.1142/s0129167x20500731
Are Austad 1 , Mads S. Jakobsen 2 , Franz Luef 1
Affiliation  

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.

中文翻译:

Morita等价C*-代数的Gabor对偶理论

Gabor 框架的对偶原理是 Gabor 分析的支柱之一。我们对具有一些额外属性的 Morita 等价双模建立了影响深远的推广。对于某些扭曲群[公式:见正文]-代数,对偶原理的重新表述为 Morita 等价双模的设置通过相对于迹的局部化而简化为著名的 Gabor 对偶原理。我们可以将模块级别的所有结果提升为矩阵代数和矩阵模块,在这样做的过程中,很自然地引入了[公式:见正文]-矩阵 Gabor 框架,它概括了多窗口超 Gabor 框架。我们还能够为等价双模上的模框架建立密度定理,这些定理定位于 [公式:见文本]-矩阵 Gabor 框架的密度定理。
更新日期:2020-05-20
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