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# Polynomial Approximation with Varying Weights on Compact Sets of the Complex Plane

Igor E. Pritsker
Proceedings of the American Mathematical Society
Vol. 126, No. 11 (Nov., 1998), pp. 3283-3292
Stable URL: http://www.jstor.org/stable/119144
Page Count: 10
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## Abstract

For a compact set E with connected complement, let A(E) be the uniform algebra of functions continuous on E and analytic interior to E. We describe A(E,W), the set of uniform limits on E of sequences of the weighted polynomials {Wn(z)Pn(z)}$_{n=0}^{\infty}$, as n → ∞ , where W ∈ A(E) is a nonvanishing weight on E. If E has empty interior, then A(E,W) is completely characterized by a zero set Z$_{W}\subset$ E. However, if E is a closure of Jordan domain, the description of A(E,W) also involves an inner function. In both cases, we exhibit the role of the support of a certain extremal measure, which is the solution of a weighted logarithmic energy problem, played in the descriptions of A(E,W).

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