Sharp upper bound for anisotropic R\'enyi entropy and Heisenberg uncertainty principle
Functional Analysis
2024-02-16 v1
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.
Keywords
Cite
@article{arxiv.2402.10003,
title = {Sharp upper bound for anisotropic R\'enyi entropy and Heisenberg uncertainty principle},
author = {Marianna Chatzakou and Michael Ruzhansky and Anjali Shriwastawa},
journal= {arXiv preprint arXiv:2402.10003},
year = {2024}
}
Comments
18 pages