Equilibrium problems associated with fast decreasing polynomials

The determination of the support of the equilibrium measure in the presence of an external field is important in the theory of weighted polynomials on the real line. Here we present a general condition guaranteeing that the s upport consists of at most two intervals. Applying this to the external fie lds associated with fast decreasing polynomials, we extend previous results of Totik and Kuijlaars-Van Assche. In the proof we use the iterated balaya ge algorithm which was first studied by Dragnev.