Proceedings of the American Mathematical Society

Polynomial approximation with varying weights on compact sets of the complex plane

Author(s): Igor E. Pritsker
Journal: Proc. Amer. Math. Soc. 126 (1998), 3283-3292.
MSC (1991): Primary 30E10; Secondary 30B60, 31A15, 41A30
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Abstract: For a compact set

with connected complement, let

be the uniform algebra of functions continuous on

and analytic interior to

We describe

the set of uniform limits on

of sequences of the weighted polynomials $\{W^n(z)P_n(z)\}_{n=0}^{\infty},$ as $n \to \infty,$ where $W \in A(E)$ is a nonvanishing weight on

has empty interior, then

is completely characterized by a zero set $Z_W \subset E.$ However, if

is a closure of Jordan domain, the description of

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

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30E10, 30B60, 31A15, 41A30

Igor E. Pritsker
Affiliation: Institute for Computational Mathematics, Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242-0001
Address at time of publication: Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7058
Email: pritsker@mcs.kent.edu, iep@po.cwru.edu

DOI: 10.1090/S0002-9939-98-04402-5
PII: S 0002-9939(98)04402-5
Keywords: Weighted polynomials, closed ideals, weighted energy problem, logarithmic potentials, uniform algebras
Received by editor(s): September 4, 1996
Received by editor(s) in revised form: March 25, 1997
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1998, American Mathematical Society

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