2025/02/17 by Shoni Gilboa, Gilboa, Shoni, Alexander Segal +3 · 1 citation
Computer Science · #26A51 #46B10 #52A41 #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2502.11524
openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.