Weighted Polynomial Approximation in the Complex Plane |
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Authors: | R. S. Varga I. E. Pritsker |
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Affiliation: | (1) Institute for Computational Mathematics (ICM), Joyce A. Fuell, Secretary, e-mail: icm@mcs.kent.edu, phone: (330) 672-2430, ext. 111 fax: (330) 672-7824, US;(2) I. E. Pritsker Institute for Computational Mathematics Department of Mathematics and Computer Science Kent State University Kent, OH 44242 USA pritsker@mcs.kent.edu , US |
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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 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. May 1, 1996. Date revised: October 8, 1996. |
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Keywords: | . Weighted polynomials Weighted energy problem Logarithmic potential Balayage Modified Robin constant. AMS Classification. 30E10 30C15 31A15 41A30. |
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