Weighted Polynomial Approximation in the Complex Plane
نویسندگان
چکیده
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 {Wn(z)Pn(z)}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.
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