Abstract
We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power [7], can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the logarithmic Sobolev inequality, and the Nash's inequality with the sharp constant.
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APA
Toscani, G. (2013). An information-theoretic proof of Nash’s inequality. Atti Della Accademia Nazionale Dei Lincei, Classe Di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 24(1), 83–93. https://doi.org/10.4171/RLM/645
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