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arXiv · 2502.11524

The Scaled Polarity transform and related inequalities

Shoni Gilboa·Alexander Segal·Boaz A. Slomka
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Abstract

In this paper we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform $\mathcal A$ 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 $\mathcal J$ transform. As an application, we extend the K\"onig-Milman duality of entropy result to the class of geometric log-concave functions.

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Shoni Gilboa, Alexander Segal, Boaz A. Slomka. 2025-02-17. The Scaled Polarity transform and related inequalities. https://doi.org/10.1007/s11784-025-01221-3

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