Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle

Takayoshi Ogawa, Kento Seraku

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The uncertainty principle of Heisenberg type can be generalized via the Boltzmann entropy functional. After reviewing the Lp generalization of the logarithmic Sobolev inequality by Del Pino-Dolbeault [6], we introduce a generalized version of Shannon's inequality for the Boltzmann entropy functional which may regarded as a counter part of the logarithmic Sobolev inequality. Obtaining best possible constants of both inequalities, we connect both the inequalities to show a generalization of uncertainty principle of the Heisenberg type.

Original languageEnglish
Pages (from-to)1651-1669
Number of pages19
JournalCommunications on Pure and Applied Analysis
Volume17
Issue number4
DOIs
Publication statusPublished - 2018 Jul

Keywords

  • Logarithmic Sobolev inequality
  • Shannon's inequality
  • The best possible constants
  • Uncertainty principle

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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