Approximation by homogeneous polynomials
- Autores: Vilmos Totik
- Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 174, Nº 1, 2013, págs. 192-205
- Idioma: inglés
- DOI: 10.1016/j.jat.2013.07.005
- Enlaces
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Resumen
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.
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