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<p>In this paper, we prove the anisotropic Shannon inequality for the Rényi 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.</p>

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Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月14日

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  • Marianna Chatzakou,
  • Michael Ruzhansky,
  • Anjali Shriwastawa

摘要

In this paper, we prove the anisotropic Shannon inequality for the Rényi 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.