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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the local asymptotics of Faber polynomials


Author: Igor E. Pritsker
Journal: Proc. Amer. Math. Soc. 127 (1999), 2953-2960
MSC (1991): Primary 30C10, 30E15; Secondary 30E10, 30C35
Published electronically: April 23, 1999
MathSciNet review: 1605937
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Abstract: We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.


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Additional Information

Igor E. Pritsker
Email: iep@po.cwru.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04891-1
PII: S 0002-9939(99)04891-1
Keywords: Faber polynomials, asymptotics, Visser-Ostrowski quotient
Received by editor(s): November 4, 1997
Received by editor(s) in revised form: December 31, 1997
Published electronically: April 23, 1999
Additional Notes: Research supported in part by the National Science Foundation grant DMS-9707359.
Dedicated: Dedicated to Professor D. Gaier on the occasion of his seventieth birthday.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1999 American Mathematical Society