The scaled polarity transform and related inequalities

Shoni Gilboa; Alexander Segal; Boaz A. Slomka

doi:10.1007/s11784-025-01221-3

The scaled polarity transform and related inequalities

Shoni Gilboa
, Alexander Segal
, Boaz A. Slomka

Mathematics

Research output: Contribution to journal › Article › peer-review

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 König–Milman duality of entropy result to the class of geometric log-concave functions.

Original language	English
Article number	73
Journal	Journal of Fixed Point Theory and Applications
Volume	27
Issue number	3
DOIs	https://doi.org/10.1007/s11784-025-01221-3
State	Published - 28 Jul 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

Access to Document

10.1007/s11784-025-01221-3

Cite this

@article{bff6fb4dbedf47b49bdf422286f933ea,

title = "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 K{\"o}nig–Milman duality of entropy result to the class of geometric log-concave functions.",

author = "Shoni Gilboa and Alexander Segal and Slomka, \{Boaz A.\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.",

year = "2025",

month = jul,

day = "28",

doi = "10.1007/s11784-025-01221-3",

language = "אנגלית",

volume = "27",

journal = "Journal of Fixed Point Theory and Applications",

issn = "1661-7738",

publisher = "Springer Science + Business Media",

number = "3",

}

TY - JOUR

T1 - The scaled polarity transform and related inequalities

AU - Gilboa, Shoni

AU - Segal, Alexander

AU - Slomka, Boaz A.

PY - 2025/7/28

Y1 - 2025/7/28

N2 - 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 König–Milman duality of entropy result to the class of geometric log-concave functions.

AB - 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 König–Milman duality of entropy result to the class of geometric log-concave functions.

UR - https://www.scopus.com/pages/publications/105011987785

U2 - 10.1007/s11784-025-01221-3

DO - 10.1007/s11784-025-01221-3

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105011987785

SN - 1661-7738

VL - 27

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 3

M1 - 73

ER -

The scaled polarity transform and related inequalities

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this