Volume 25, pp. 278-283, 2006.

A note on the sharpness of the Remez-type inequality for homogeneous polynomials on the sphere

M. Yattselev

Abstract

Remez-type inequalities provide upper bounds for the uniform norms of polynomials $p$ on given compact sets $K,$ provided that $|p(x)|\leq1$ for every $x\in K\setminus E,$ where $E$ is a subset of $K$ of small measure. In this note we obtain an asymptotically sharp Remez-type inequality for homogeneous polynomials on the unit sphere in ${\bf R}^d.$

Full Text (PDF) [150 KB]

Key words

Remez-type inequalities, homogeneous polynomials

AMS subject classifications

41A17

< Back