The geometry of Euclidean convolution inequalities and entropy
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- by Dario Cordero-Erausquin and Michel Ledoux PDF
- Proc. Amer. Math. Soc. 138 (2010), 2755-2769 Request permission
Abstract:
The goal of this paper is to show that some convolution type inequalities from Harmonic Analysis and Information Theory, such as Young’s convolution inequality (with sharp constant), Nelson’s hypercontractivity of the Hermite semi-group or Shannon’s inequality, can be reduced to a simple geometric study of frames of $\mathbb {R}^2$. We shall derive directly entropic inequalities, which were recently proved to be dual to the Brascamp-Lieb convolution type inequalities.References
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Additional Information
- Dario Cordero-Erausquin
- Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6), 4 place Jussieu, 75252 Paris Cedex 05, France
- Email: cordero@math.jussieu.fr
- Michel Ledoux
- Affiliation: Institut de Mathématiques de Toulouse, Université de Toulouse, 31062 Toulouse, France
- MR Author ID: 111670
- Email: ledoux@math.univ-toulouse.fr
- Received by editor(s): July 16, 2009
- Published electronically: April 21, 2010
- Communicated by: Marius Junge
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2755-2769
- MSC (2010): Primary 42A85, 52A40, 60E15; Secondary 60G15, 94A17
- DOI: https://doi.org/10.1090/S0002-9939-10-10304-9
- MathSciNet review: 2644890