Abstract.
Let G\subset C be a finite domain with a regular Jordan boundary L . In this work, the approximation properties of a p -Faber polynomial series of functions in the weighted Smirnov class E p (G,ω) are studied and the rate of polynomial approximation, for f∈ E p ( G,ω) by the weighted integral modulus of continuity, is estimated. Some application of this result to the uniform convergence of the Bieberbach polynomials π n in a closed domain \overline G with a smooth boundary L is given.
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February 25, 1999. Date revised: October 20, 1999. Date accepted: May 26, 2000.
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Israfilov, D. Approximation by p -Faber polynomials in the weighted Smirnov class Ep( G,ω ) and the Bieberbach polynomials. Constr. Approx. 17, 335–351 (2001). https://doi.org/10.1007/s003650010030
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DOI: https://doi.org/10.1007/s003650010030
- Key words
- Faber polynomials
- Weighted Smirnov class
- Bieberbach polynomials
- Conformal mapping
- Uniform convergence