Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle
arxiv(2024)
Abstract
In this paper, we prove the anisotropic Shannon inequality for the Renyi
entropy with the best constant on Folland-Stein homogeneous Lie groups. As a
consequence, we also prove the optimal Shannon inequality in the same setting.
Using a logarithmic Sobolev inequality in the setting of stratified groups, we
prove a Heisenberg-type uncertainty principle in the latter setting.
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