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arXiv · 2402.10003

Sharp upper bound for anisotropic R\'enyi entropy and Heisenberg uncertainty principle

Marianna Chatzakou·Michael Ruzhansky·Anjali Shriwastawa
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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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Marianna Chatzakou, Michael Ruzhansky, Anjali Shriwastawa. 2024-02-15. Sharp upper bound for anisotropic R\'enyi entropy and Heisenberg uncertainty principle. https://arxiv.org/abs/2402.10003

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