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Bibliographic Details
Main Authors: Gilboa, Shoni, Segal, Alexander, Slomka, Boaz A.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.11524
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author Gilboa, Shoni
Segal, Alexander
Slomka, Boaz A.
author_facet Gilboa, Shoni
Segal, Alexander
Slomka, Boaz A.
contents 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 König-Milman duality of entropy result to the class of geometric log-concave functions.
format Preprint
id arxiv_https___arxiv_org_abs_2502_11524
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Scaled Polarity transform and related inequalities
Gilboa, Shoni
Segal, Alexander
Slomka, Boaz A.
Functional Analysis
52A41, 26A51, 46B10
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 König-Milman duality of entropy result to the class of geometric log-concave functions.
title The Scaled Polarity transform and related inequalities
topic Functional Analysis
52A41, 26A51, 46B10
url https://arxiv.org/abs/2502.11524