The geometry of Euclidean convolution inequalities and entropy

Details The geometry of Euclidean convolution inequalities and entropy The geometry of Euclidean convolution inequalities and entropy

2009-07-16

arxiv.org/abs/0907.2861v1

Mathematics

Functional Analysis

Scientific paper

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.

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