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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The support of the equilibrium measure in the presence of a monomial external field on $[-1,1]$


Authors: S. B. Damelin and A. B. J. Kuijlaars
Journal: Trans. Amer. Math. Soc. 351 (1999), 4561-4584
MSC (1991): Primary 31A15; Secondary 41A10, 45E05.
Published electronically: July 21, 1999
MathSciNet review: 1675178
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Abstract: The support of the equilibrium measure associated with an external field of the form $Q(x) = - cx^{2m+1}$, $x \in [-1,1]$, with $c > 0$ and $m$ a positive integer is investigated. It is shown that the support consists of at most two intervals. This resolves a question of Deift, Kriecherbauer and McLaughlin.


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Additional Information

S. B. Damelin
Affiliation: Department of Mathematics, University of the Witwatersrand, PO Wits 2050, South Africa
Email: 036sbd@cosmos.wits.ac.za

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

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02509-X
PII: S 0002-9947(99)02509-X
Keywords: Balayage, equilibrium measure, external field, potential theory, weighted polynomials
Received by editor(s): June 22, 1997
Published electronically: July 21, 1999
Additional Notes: The research of the first author was begun while visiting the Mathematics Department at the Katholieke Universiteit Leuven, whose invitation to visit and hospitality are kindly acknowledged. This research was partly financed by FWO research project G.0278.97.
The second author was 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
Article copyright: © Copyright 1999 American Mathematical Society