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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