# Extremal and approximation problems for positive definite functions

Seminar
Speaker
Dr. Panagiotis Mavroudis, University of Crete, Greece
Date
21/12/2015 - 20:35 - 14:00Add to Calendar 2015-12-21 14:00:00 2015-12-21 20:35:00 Extremal and approximation problems for positive definite functions Let $\Omega$ be an open 0-symmetric subset of $\mathbb R^d$ which contains 0 and f a continuous positive definite function vanishing off O, that is, supp f is contained in the closure of $\Omega$. The problem is to approximate f by a continuous positive definite function F supported in $\Omega$. We prove this when 1. d=1. 2 $\Omega$ is strictly star-shaped 3. f is a radial function. We also consider the following problem: Given a measure $\mu$ supported in $\Omega$, does  there exist an extremal function for the problem $\sup \int f d\mu$, where the sup is taken over the cone of continuous  positive definite functions f supported in $\Omega$ with f(0)=1? 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

Let $\Omega$ be an open 0-symmetric subset of $\mathbb R^d$ which contains 0 and
f a continuous positive definite function vanishing off O, that is,
supp f is contained in the closure of $\Omega$. The problem is to approximate
f by a continuous positive definite function F supported in $\Omega$. We prove
this when 1. d=1. 2 $\Omega$ is strictly star-shaped 3. f is a radial function.
We also consider the following problem: Given a measure $\mu$
supported in $\Omega$, does  there exist an extremal function for the problem
$\sup \int f d\mu$, where the sup is taken over the cone of continuous
positive definite functions f supported in $\Omega$ with f(0)=1?

תאריך עדכון אחרון : 15/12/2015