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 suficient 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 in [−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.

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