Geodesic
Weighted polynomial approximation in the complex plane
Pritsker, Igor1 ; Varga, Richard1
1 Institute for Computational Mathematics, Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242-0001
Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 38-44 Cet article a éte moissonné depuis la source American Mathematical Society

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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 $\left \{W^{n}(z)P_{n}(z) \right \}^{\infty }_{n=0}$, where $\deg P_{n} \leq n$. 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.
DOI : 10.1090/S1079-6762-97-00021-8

Pritsker, Igor 1 ; Varga, Richard 1

1 Institute for Computational Mathematics, Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242-0001 
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Pritsker, Igor; Varga, Richard. Weighted polynomial approximation in the complex plane. Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 38-44. doi: 10.1090/S1079-6762-97-00021-8

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