Related papers: Partitions and functional Santalo inequalities
In this paper, using functional Steiner symmetrizations, we show that Meyer and Pajor's proof of the Blaschke-Santalo inequality can be extended to the functional setting.
We give a simple proof of a functional version of the Blaschke-Santalo inequality due to Artstein, Klartag and Milman. The proof is by induction on the dimension and does not use the Blaschke-Santalo inequality.
In 2024, Courtade, Fathi and Mikulincer gave a proof of the symmetrized Talagrand inequality based on stochastic calculus, in the spirit of Borell's proof of the Pr\'ekopa-Leindler inequality. The symmetrized Talagrand inequality can be…
In this work we establish functional asymmetric versions of the celebrated Blaschke-Santal\'o inequality. As consequences of these inequalities we recover their geometric counterparts with equality cases, as well as, another inequality with…
We establish new functional versions of the Blaschke-Santal\'o inequality on the volume product of a convex body which generalize to the non-symmetric setting an inequality of K. Ball and we give a simple proof of the case of equality. As a…
Motivated by the geodesic barycenter problem from optimal transportation theory, we prove a natural generalization of the Blaschke-Santalo inequality and the affine isoperimetric inequalities for many sets and many functions. We derive from…
Stability versions of the functional forms of the Blaschke-Santalo inequality due to Ball, Artstein-Klartag-Milman, Fradelizi-Meyer and Lehec are proved.
We present an abstract form of the Pr\'ekopa-Leindler inequality that includes several known -and a few new- related functional inequalities on Euclidean spaces. The method of proof and also the formulation of the new inequalities are based…
The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
In this paper, we present a simple proof of a recent result of the second author which establishes that functional inverse-Santal{\'o} inequalities follow from Entropy-Transport inequalities. Then, using transport arguments together with…
In this paper, we study new extensions of the functional Blaschke-Santalo inequalities, and explore applications of such new inequalities beyond the classical setting of the standard Gaussian measure.
It is shown that each monotone Minkowski endomorphism of convex bodies gives rise to an isoperimetric inequality which directly implies the classical Urysohn inequality. Among this large family of new inequalities, the only affine invariant…
In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix…
We show that many theorems which assert that two kinds of partitions of the same integer $n$ are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics $X$ and…
We prove a conjecture of Cuttler et al.~[2011] [A. Cuttler, C. Greene, and M. Skandera; \emph{Inequalities for symmetric means}. European J. Combinatorics, 32(2011), 745--761] on the monotonicity of \emph{normalized Schur functions} under…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santal\'o inequality in its functional form. Inspired by their method, based on the…
We discuss a topological structure on families of convex functions and then apply it to show the existence of extrimizers for the functional Santal\'{o} inequality with respect to polar transform and its reverse.
We provide a fractional counterpart of the classical results by Schwarz and Malmheden on harmonic functions. From that we obtain a representation formula for $s$-harmonic functions as a linear superposition of weighted classical harmonic…