Density of Multivariate Polynomials on Convex and Star like domains

Type: 
PhD Student Seminar
Audience: 
Open to the Public
Building: 
Zrinyi u. 14
Room: 
310/A
Wednesday, March 19, 2014 - 2:00pm
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Date: 
Wednesday, March 19, 2014 - 2:00pm to 3:30pm

Abstract: A central question in Approximation Theory concerns the
possibility of approximation of continuous functions by various
families of polynomials, that is density of classes of polynomials. On
one hand the density of a given polynomial family depends on the
algebraic structure of this set. In addition, in the multivariate case
the question of density is also intricately related to the geometric
properties of the underlying domain on which the approximation is
studied.

In the present talk we shall explore this interplay between algebraic
and geometric properties in the study of density of various families
of multivariate polynomials on compact subsets of R^d, in particular
convex bodies or star like domains. The families of polynomials will
include multivariate homogeneous polynomials, convex polynomials and
incomplete polynomials.

You can watch the lecture here:

https://www.youtube.com/watch?v=ml3gLjZCcxQ&index=5&list=PL_0phSnA7tyQJD...