Published at: Journal of fixed theory and applications

The scaled polarity transform and related inequalities

Abstract

In this paper, we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform 𝒜 can be rescaled so that the Mahler product it induces has upper and lower bounds of the same asymptotics. We discuss a similar result for the 𝒥 transform. As an application, we extend the Koenig-Milman duality of entropy result to the class of geometric log-concave functions.

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