Weighted Approximation on Compact Sets
نویسنده
چکیده
For a compact set E with connected complement in the com plex plane we consider a problem of the uniform approximation on E by the weighted polynomials W z Pn z where W z is a continuous non vanishing weight function on E analytic in the interior of E Let A E W be the set of functions uniformly approximable on E by such weighted polynomials If E has empty interior then A E W is completely char acterized by a zero set ZW E where all functions from A E W must vanish This generalizes recent results of Totik and Kuijlaars for the real line case 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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