TY - JOUR
T1 - The scaled polarity transform and related inequalities
AU - Gilboa, Shoni
AU - Segal, Alexander
AU - Slomka, Boaz A.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.
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
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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 -