Weighted polynomial approximation in the complex plane

Authors:
Igor E. Pritsker and Richard S. Varga

Journal:
Electron. Res. Announc. Amer. Math. Soc. **3** (1997), 38-44

MSC (1991):
Primary 30E10; Secondary 30C15, 31A15, 41A30

DOI:
https://doi.org/10.1090/S1079-6762-97-00021-8

Published electronically:
May 2, 1997

MathSciNet review:
1445633

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a pair of an open bounded set in the complex plane and a weight function which is analytic and different from zero in , we consider the problem of the locally uniform approximation of any function , which is analytic in , by weighted polynomials of the form , where . 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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Additional Information

**Igor E. Pritsker**

Affiliation:
Institute for Computational Mathematics, Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242-0001

Email:
pritsker@mcs.kent.edu

**Richard S. Varga**

Affiliation:
Institute for Computational Mathematics, Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242-0001

Email:
varga@mcs.kent.edu

DOI:
https://doi.org/10.1090/S1079-6762-97-00021-8

Keywords:
Weighted polynomials,
locally uniform approximation,
logarithmic potential,
balayage

Received by editor(s):
October 15, 1996

Published electronically:
May 2, 1997

Communicated by:
Yitzhak Katznelson

Article copyright:
© Copyright 1997
American Mathematical Society