Abstract.
It is proven that if Q is convex and w(x)= exp(-Q(x)) is the corresponding weight, then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form w n P n . This solves a problem of P. Borwein and E. B. Saff. Actually, a similar result is true locally for any parts of the extremal support where Q is convex.
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February 10, 1998. Date revised: July 23, 1998. Date accepted: August 17, 1998.
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Totik, V. Weighted Polynomial Approximation for Convex External Fields . Constr. Approx. 16, 261–281 (2000). https://doi.org/10.1007/s003659910011
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DOI: https://doi.org/10.1007/s003659910011