Abstract

It is shown that a conjecture of E.A. Rakhmanov is true concerning the zero distribution of orthogonal polynomials with respect to a measure having a discrete real support. We also discuss the case of extremal polynomials with respect to some discrete $L_p$--norm, $0 < p leq infty$, and give an extension to complex supports.

Furthermore, we present properties of weighted Fekete points with respect to discrete complex sets, such as the weighted discrete transfinite diameter and a weighted discrete Bernstein--Walsh--like inequality.