# Extremal and approximation problems for positive definite functions

Mon, 21/12/2015 - 14:00

Speaker:

Dr. Panagiotis Mavroudis, University of Crete, Greece

Seminar:

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?

- Last modified: 15/12/2015