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

Damelin, S.; Kuijlaars, A.

doi:10.1090/S0002-9947-99-02509-X

The support of the equilibrium measure in the presence of a monomial external field on $[-1,1]$
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by S. B. Damelin and A. B. J. Kuijlaars

Trans. Amer. Math. Soc. 351 (1999), 4561-4584

DOI: https://doi.org/10.1090/S0002-9947-99-02509-X

Published electronically: July 21, 1999

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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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