Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The geometry of Euclidean convolution inequalities and entropy

Author(s): Dario Cordero-Erausquin; Michel Ledoux
Journal: Proc. Amer. Math. Soc. 138 (2010), 2755-2769.
MSC (2010): Primary 42A85, 52A40, 60E15; Secondary 60G15, 94A17
Posted: April 21, 2010
Previous version: Original version posted March 26, 2010
Corrected version: Current version corrects publisher's introduction of $=\mu_2$ in the first sentence of the fourth paragraph and the introduction of $_n$ at the end of the second line of the fifth paragraph.
MathSciNet review: 2644890
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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.

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