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Uncertainty Principles for the Hankel-Gabor Transform
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2020-03-13 , DOI: 10.1007/s13226-020-0398-4 Aymen Hammami
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2020-03-13 , DOI: 10.1007/s13226-020-0398-4 Aymen Hammami
In this paper, we prove an analogue of a time-frequency localization theorem for orthonormal sequences in \(L_{{\mu _\alpha }}^2({\mathbb{R}_ + })\). As a consequence, we obtain an analogue of Shapiro’s Umbrella theorem for the Hankel-Gabor transform Vg. We also prove a mean dispersion inequality for Vg. Finally, we get a strong version of the uncertainty inequality for orthonormal sequences of \(L_{{\mu _\alpha }}^2({\mathbb{R}_ + })\).
中文翻译:
Hankel-Gabor变换的不确定性原理
在本文中,我们证明了\(L _ {{\ mu _ \ alpha}} ^ 2({\ mathbb {R} _ +})\)\中的正交序列的时频定位定理的类似物。结果,我们获得了汉克尔-加伯变换V g的夏皮罗伞定理的类似物。我们还证明了V g的平均色散不等式。最后,我们得到\(L _ {{\ mu _ \ alpha}} ^ 2({\ mathbb {R} _ +})\)的正交序列的不确定性不等式的强版本。
更新日期:2020-03-13
中文翻译:
Hankel-Gabor变换的不确定性原理
在本文中,我们证明了\(L _ {{\ mu _ \ alpha}} ^ 2({\ mathbb {R} _ +})\)\中的正交序列的时频定位定理的类似物。结果,我们获得了汉克尔-加伯变换V g的夏皮罗伞定理的类似物。我们还证明了V g的平均色散不等式。最后,我们得到\(L _ {{\ mu _ \ alpha}} ^ 2({\ mathbb {R} _ +})\)的正交序列的不确定性不等式的强版本。