Weierstrass Theorem for homogeneous polynomials on convex bodies and rate of approximation of convex bodies by convex algebraic level surfaces

Analysis Seminar
Tuesday, November 29, 2011 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Hungarian Academy of Sciences
By the classical Weierstrass theorem, any function continuous on a compact set can be uniformly approximated by algebraic polynomials. In this talk we shall discuss possible extensions of this basic result of analysis to approximation by homogeneous algebraic polynomials on central symmetric convex bodies. We shall also consider a related question of approximating convex bodies by convex algebraic level surfaces. It has been known for some time time that any convex body can be approximated arbitrarily well by convex algebraic level surfaces. We shall present in this talk some new results specifying rate of convergence.