Extremal problems of Chebyshev type

Author:
Franz Peherstorfer

Journal:
Proc. Amer. Math. Soc. **137** (2009), 2351-2361

MSC (2000):
Primary 41A29; Secondary 33C45, 41A60

Published electronically:
January 13, 2009

MathSciNet review:
2495269

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be given. We consider the problem of finding among all polynomials with complex coefficients of degree less than or equal to with . We derive an asymptotic expression for the extremal polynomial and for the extremal value in terms of elementary functions. The solution is based on the description of Zolotarev polynomials with respect to square root polynomial weights.

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Additional Information

**Franz Peherstorfer**

Affiliation:
Abteilung für Dynamische Systeme und Approximationstheorie, Institut für Analysis, Johannes Kepler Universität Linz, Altenberger Strasse, 69, 4040 Linz, Austria

Email:
franz.peherstorfer@jku.at

DOI:
http://dx.doi.org/10.1090/S0002-9939-09-09771-8

Received by editor(s):
December 4, 2007

Received by editor(s) in revised form:
September 18, 2008

Published electronically:
January 13, 2009

Additional Notes:
The author was supported by the Austrian Science Fund FWF, project no. P20413-N18

Communicated by:
Peter A. Clarkson

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.