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

DOI: 10.2140/pjm.2001.199.303

Abstract

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.

Milestones

Received: 16 July 1999

Revised: 11 October 2000

Published: 1 June 2001