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

@article{Ogawa2018LogarithmicSA,
title={Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle},
author={Takayoshi Ogawa and Kento Seraku},
journal={Communications on Pure and Applied Analysis},
year={2018},
volume={17},
pages={1651-1669}
}
• Published 1 April 2018
• Mathematics
• Communications on Pure and Applied Analysis
The uncertainty principle of Heisenberg type can be generalized via the Boltzmann entropy functional. After reviewing the \begin{document} $L^p$ \end{document} 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…
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