Abstract.
Given a pair (G,W) of an open bounded set G in the complex plane and a weight function W(z) which is analytic and different from zero in G , we consider the problem of the locally uniform approximation of any function f(z) , which is analytic in G , by weighted polynomials of the form {W n (z)P n (z) } $\infinity$ n=0 , where deg Pn \(\leq\)n. The main result of this paper is a necessary and sufficient condition for such an approximation to be valid. We also consider a number of applications of this result to various classical weights, which give explicit criteria for these weighted approximations.
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May 1, 1996. Date revised: October 8, 1996.
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Varga, R., Pritsker, I. Weighted Polynomial Approximation in the Complex Plane. Constr. Approx. 14, 475–492 (1998). https://doi.org/10.1007/s003659900086
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DOI: https://doi.org/10.1007/s003659900086