Abstract
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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The authors would like to thank the referee for having suggested valuable comments to improve the final form of the paper.
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Smaoui, K., Abid, K. Heisenberg uncertainty inequality for Gabor transform on nilpotent Lie groups. Anal Math 48, 147–171 (2022). https://doi.org/10.1007/s10476-021-0112-8
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DOI: https://doi.org/10.1007/s10476-021-0112-8