e-mail: DragnevP@IPFW.EDU

**The Support of the Equilibrium Measure for a Class
of External Fields on a Finite Interval**

(Joint work with S. B. Damelin and A. B. J. Kuijlaars.)

**Abstract**

We investigate the support of the equilibrium measure associated with
a class of nonconvex, nonsmooth (i.e. non real analytic 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 $-c \,{\sign}(x) |x|^{\alpha}$
with $c > 0$, $\alpha \geq 1$ and $x \in [-1,1]$.
If $\alpha$ 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.