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

DOI10.3934/cpaa.2018079zbMath1395.42067OpenAlexW2796395469MaRDI QIDQ1659617

Kento Seraku, Takayoshi Ogawa

Publication date: 22 August 2018

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2018079

zbMATH Keywords

logarithmic Sobolev inequalityuncertainty principleShannon's inequalitythe best possible constants

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Inequalities involving derivatives and differential and integral operators (26D10) Harmonic analysis and PDEs (42B37)

Related Items (5)

Shannon's inequality for the Rényi entropy and an application to the uncertainty principle ⋮ Uncertainty principles for the coupled fractional Wigner distribution ⋮ Shannon, Sobolev and uncertainty inequalities for the Weinstein transform ⋮ Beckner type of the logarithmic Sobolev and a new type of Shannon’s inequalities and an application to the uncertainty principle ⋮ Sharp Shannon's and logarithmic Sobolev inequalities for the Hankel transform

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