Vol. 199, No. 2, 2001

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The support of the equilibrium measure for a class of external fields on a finite interval

S.B. Damelin, P.D. Dragnev and A.B.J. Kuijlaars

Vol. 199 (2001), No. 2, 303–320

We investigate the support of the equilibrium measure associated with a class of nonconvex, nonsmooth external fields on a finite interval. Such equilibrium measures play an important role in various branches of analysis. In this paper we obtain a sufficient condition which ensures that the support consists of at most two intervals. This is applied to external fields of the form csign(x)|x|α with c > 0, α 1 and x [1,1]. If α is an odd integer, these external fields are smooth, and for this case the support was studied before by Deift, Kriecherbauer and McLaughlin, and by Damelin and Kuijlaars.

Received: 16 July 1999
Revised: 11 October 2000
Published: 1 June 2001
S.B. Damelin
Department of Mathematics and Computer Science
Georgia Southern University
Statesboro, Georgia, 30460-8093
P.D. Dragnev
Department of Mathematical Sciences
Indiana University–Purdue University
Fort Wayne, IN 46805
A.B.J. Kuijlaars
Department of Mathematics
Katholieke Universiteit Leuven
Celestijnenlaan 200 B
3001 Leuven