Resumen de Approximation by homogeneous polynomials

Vilmos Totik

• A new, elementary proof is given for the fact that on a centrally symmetric convex curve on the plane every continuous even function can be uniformly approximated by homogeneous polynomials. The theorem has been proven before by Benko and Kro´o, and independently by Varj´u using the theory of weighted potentials. In higher dimension the new method recaptures a theorem of Kro´o and Szabados, which is the strongest result for homogeneous polynomial approximation on smooth convex surfaces.