An information-theoretic proof of Nash's inequality
type: Item
instance of: scholarly article
title: An information-theoretic proof of Nash's inequality
zbMATH Open document ID: 1301.62006
DOI: 10.4171/RLM/645
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2013-06-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1206.2130
review text: Summary: We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power [\textit{M. H. M. Costa}, IEEE Trans. Inf. Theory 31, 751--760 (1985; Zbl 0585.94006)], 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.
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 94A15
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 6179928
zbMATH Keywords: entropy power
zbMATH Keywords: Fisher information
zbMATH Keywords: logarithmic Sobolev inequality
zbMATH Keywords: Nash's inequality
author: G. Toscani
MaRDI profile type: Publication
arXiv ID: 1206.2130
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description: scientific article