Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 263657, 8 pages
http://dx.doi.org/10.5402/2011/263657
Research Article

On the Asymptotic Behavior of p-Faber Polynomials for Domains with Piecewise Analytic Boundary

Department of Mathematics, Mersin University, 3343 Mersin, Turkey

Received 3 July 2011; Accepted 8 August 2011

Academic Editor: X.-L. Gao

Copyright © 2011 T. Tunc and M. Kucukaslan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let 𝐺 βŠ‚ β„‚ be a domain bounded by a piecewise analytic Jordan's curve L, and let 𝐹 𝑛 , 𝑝 denote the p-Faber polynomials associated with G. We derive estimates of the form 𝐹 𝑛 , 𝑝 ( 𝑧 ) = 𝑂 ( 1 / 𝑛 πœ‚ ) , ( 𝑛 β†’ ∞ ) for 𝑧 ∈ 𝐺 , where πœ‚ depends on geometric properties of L and the parameter p. Also, we show that O cannot be replaced by o in the relation given above.