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

 

Equilibrium problems associated
with fast decreasing polynomials


Authors: A. B. J. Kuijlaars and P. D. Dragnev
Journal: Proc. Amer. Math. Soc. 127 (1999), 1065-1074
MSC (1991): Primary 41A10, 31A15
MathSciNet review: 1469419
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Abstract: The determination of the support of the equilibrium measure in the presence of an external field is important in the theory of weighted polynomials on the real line. Here we present a general condition guaranteeing that the support consists of at most two intervals. Applying this to the external fields associated with fast decreasing polynomials, we extend previous results of Totik and Kuijlaars-Van Assche. In the proof we use the iterated balayage algorithm which was first studied by Dragnev.


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Additional Information

A. B. J. Kuijlaars
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Email: arno@wis.kuleuven.ac.be

P. D. Dragnev
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620
Address at time of publication: Department of Mathematical Sciences, Indiana University Purdue University Fort Wayne, Fort Wayne, Indiana 46805
Email: dragnevp@ipfw.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04590-6
PII: S 0002-9939(99)04590-6
Keywords: Equilibrium measures, extremal support, balayage, fast decreasing polynomials
Received by editor(s): December 12, 1996
Received by editor(s) in revised form: July 16, 1997
Additional Notes: The first author is supported by a postdoctoral fellowship of the Belgian National Fund for Scientific Research, Scientific Research Network nr WO.011.96N: Fundamental Methods and Techniques in Mathematics. The research of the second author is in partial fulfillment of the Ph.D. requirements at the University of South Florida.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1999 American Mathematical Society