This is an announcement for the paper "The geometry of Euclidean convolution inequalities and entropy" by Dario Cordero-Erausquin and Michel Ledoux.

Abstract: The goal of this note 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 $\R^2$. We shall derive directly entropic inequalities, which were recently proved to be dual to the Brascamp-Lieb convolution type inequalities.

Archive classification: math.FA math.PR

The source file(s), geoconv5.tex: 49291 bytes, is(are) stored in gzipped form as 0907.2861.gz with size 16kb. The corresponding postcript file has gzipped size 113kb.

Submitted from: cordero@math.jussieu.fr

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http://front.math.ucdavis.edu/0907.2861

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http://arXiv.org/abs/0907.2861

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