اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBlaschke-Santalo inequality for many functions and geodesic barycenters of measures
86
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 it an entropy bound for the total Kantorovich cost appearing in the barycenter problem. We also establish a pointwise Prekopa-Leindler inequality and show a monotonicity property of the multimarginal Blaschke-Santalo functional.
قيم البحث
اقرأ أيضاً
In this paper we consider the so-called procedure of {it Continuous Steiner Symmetrization}, introduced by Brock in cite{bro95,bro00}. It transforms every domain $Omegasubsetsubsetmathbb{R}^d$ into the ball keeping the volume fixed and letting the fi
rst eigenvalue and the torsion respectively decrease and increase. While this does not provide, in general, a $gamma$-continuous map $tmapstoOmega_t$, it can be slightly modified so to obtain the $gamma$-continuity for a $gamma$-dense class of domains $Omega$, namely, the class of polyedral sets in $mathbb{R}^d$. This allows to obtain a sharp characterization of the Blaschke-Santalo diagram of torsion and eigenvalue.
We analyze the fine structure of Clark measures and Clark isometries associated with two-variable rational inner functions on the bidisk. In the degree (n,1) case, we give a complete description of supports and weights for both generic and exceptiona
l Clark measures, characterize when the associated embedding operators are unitary, and give a formula for those embedding operators. We also highlight connections between our results and both the structure of Agler decompositions and study of extreme points for the set of positive pluriharmonic measures on 2-torus.
In 2000 V. Lomonosov suggested a counterexample to the complex version of the Bishop-Phelps theorem on modulus support functionals. We discuss the $c_0$-analog of that example and demonstrate that the set of sup-attaining functionals is non-trivial,
thus answering an open question, asked in cite{KLMW}.
In this article, we prove a Strichartz type inequality %associated with Schrodinger equation for a system of orthonormal functions associated with the special Hermite operator $mathcal{L}=-Delta+frac{1}{4}|z|^{2}-i sum_{1}^{n}left(x_{j} frac{partial}
{partial y_{j}}-y_{j} frac{partial}{partial x_{j}}right), $ where $Delta$ denotes the Laplacian on $mathbb{C}^{n}$.
The Strichartz inequality for the system of orthonormal functions for the Hermite operator $H=-Delta+|x|^2$ on $mathbb{R}^n$ has been proved in cite{lee}, using the classical Strichartz estimates for the free Schrodinger propagator for orthonormal sy
stems cite{frank, frank1} and the link between the Schrodinger kernel and the Mehler kernel associated with the Hermite semigroup cite{SjT}. In this article, we give an alternative proof of the above result in connection with the restriction theorem with respect to the Hermite transform with an optimal behavior of the constant in the limit of a large number of functions. As an application, we show the well-posedness results in Schatten spaces for the nonlinear Hermite-Hartree equation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
