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Gabor Duals for Operator-valued Gabor Frames on Locally Compact Abelian Groups
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) ( IF 0.3 ) Pub Date : 2019-12-27 , DOI: 10.3103/s1068362319060025
Y. Hu , P. Li

Motivated by the ordinary Gabor frames in L2(ℝd) and operator-valued frames on abstract Hilbert spaces, we investigate operator-valued Gabor frames associated with locally compact Abelian groups. Necessary and sufficient conditions for an operator-valued Gabor frame to admit a Parseval/tight Gabor dual are given. In particular, we consider a special case, which includes the case of ordinary Gabor frames.



中文翻译:

局部紧的阿贝尔群上算子值Gabor框架的Gabor对偶

通过在普通的Gabor帧动机大号2(ℝ d)和抽象Hilbert空间算子值的帧中,我们研究与局部紧交换群相关联的算子值的Gabor帧。给出了操作员值Gabor框架接受Parseval /紧Gabor对偶的充要条件。特别地,我们考虑一种特殊情况,其中包括普通Gabor框架的情况。

更新日期:2019-12-27
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