Abstract
In this paper we study the extremal polynomials for the Markov inequality on a convex symmetric body K⊂Rm, that is, norm 1 polynomials on K whose gradients attain the largest value on K. It is shown that any such polynomial must coincide with the Chebyshev polynomial along a certain line. Moreover, this fact is applied to the study of uniqueness of extremal polynomials.
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