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

Author:
Igor E. Pritsker

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3283-3292

MSC (1991):
Primary 30E10; Secondary 30B60, 31A15, 41A30

MathSciNet review:
1452821

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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 as where is a nonvanishing weight on If has empty interior, then is completely characterized by a zero set 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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Additional Information

**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:
http://dx.doi.org/10.1090/S0002-9939-98-04402-5

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

Article copyright:
© Copyright 1998
American Mathematical Society