On a conjecture of E. A. Rakhmanov

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 less than or equal to infinity, 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.