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On Polynomials with a Prescribed Zero on a Quasicircle

On Polynomials with a Prescribed Zero on a Quasicircle Let G ∈ ℂ be a Jordan domain and P a polynomial of degree at most n, satisfying ¦P(z)¦ ≤1 for z ∈ G and P(z(in1)) = 0, where z 1 ∈ ∂G. If G is bounded by a quasiconformal curve we asymptotically estimate ¦P(z 0)¦, where z 0 ∈ G. In case z 1 is on a sufficiently smooth portion of ∂G, our results correspond to the previous ones by Halász for the special case G = D, the unit disk. We also obtain complete results in case z 1 corresponds to a corner of ∂G. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On Polynomials with a Prescribed Zero on a Quasicircle

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321686
Publisher site
See Article on Publisher Site

Abstract

Let G ∈ ℂ be a Jordan domain and P a polynomial of degree at most n, satisfying ¦P(z)¦ ≤1 for z ∈ G and P(z(in1)) = 0, where z 1 ∈ ∂G. If G is bounded by a quasiconformal curve we asymptotically estimate ¦P(z 0)¦, where z 0 ∈ G. In case z 1 is on a sufficiently smooth portion of ∂G, our results correspond to the previous ones by Halász for the special case G = D, the unit disk. We also obtain complete results in case z 1 corresponds to a corner of ∂G.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jul 25, 2009

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