Approximation by homogeneous polynomials

作者：Totik Vilmos^*

来源：Journal of Approximation Theory, 2013, 174: 192-205.

DOI：10.1016/j.jat.2013.07.005

• Homogeneous polynomials
• Approximation
• Convex surfaces and curves

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 Kroo, and independently by Varju using the theory of weighted potentials. In higher dimension the new method recaptures a theorem of Kroo and Szabados, which is the strongest result for homogeneous polynomial approximation on smooth convex surfaces.

• 出版日期2013-10