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

DOI:
https://doi.org/10.1090/S0002-9939-99-04590-6

MathSciNet review:
1469419

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-99-04590-6

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