Heisenberg uncertainty inequality for Gabor transform on nilpotent Lie groups

被引：0
作者：
K. Smaoui
K. Abid
机构：
[1] Sfax University,Higher Institute of Information Technology and Multimedia, Pôle Technologique de Sfax
[2] Sfax University,Faculty of Sciences
来源：
Analysis Mathematica | 2022年 / 48卷
关键词：
Heisenberg uncertainty inequality; nilpotent Lie group; Gabor transform; Plancherel formula; primary 22E25; secondary 43A25; 43A32;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we define and prove an analog of the Heisenberg uncertainty inequality for Gabor transform in the setup of connected, simply connected nilpotent Lie groups. When G is connected nilpotent and has a non-compact center, a proof of such an analog is given for functions in the Schwartz space of G. The representation theory and a localized Plancherel formula are fundamental tools in the proof of our results.
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页码：147 / 171
页数：24
相关论文
共 23 条
[1]  
Bonami A(2003)Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms Rev. Mat. Iberoam. 19 23-55
[2]  
Demange B(2016)Heisenberg uncertainty inequality for Gabor transform J. Math. Inequal. 10 737-749
[3]  
Jaming P(2003)Estimate of J. Funct. Anal. 199 508-520
[4]  
Bansal A(2007)-Fourier transform norm on nilpotent Lie groups Adv. Math. 215 616-625
[5]  
Kumar A(1998)Heisenberg—Pauli—Weyl uncertainty inequalities and polynomial volume growth J. Math. Phys. 39 4016-4040
[6]  
Baklouti A(2012)Separability, positivity, and minimum uncertainty in time-frequency energy distributions Bull. Belg. Math. Soc. Simon Stevin 19 683-701
[7]  
Smaoui K(1991)Continuous Gabor transform for a class of non-Abelian groups IEEE Trans. Inform. Theory 39 202-204
[8]  
Ludwig J(2001)Optimality property of the gaussian window spectrogram Math. Proc. Camb. Philos. Soc. 131 487-494
[9]  
Ciatti P(2018)Hardy’s theorem for nilpotent Lie groups Int. J. Math. 29 1850086-145
[10]  
Ricci F(2019)Heisenberg—Pauli—Weyl inequality for connected nilpotent Lie groups Asian-European J. Math. 12 1950065-226
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