On a conjecture of E. A. Rakhmanov

It is shown that a conjecture of E. A. Rakhmanov is true concerning the zer o distribution of orthogonal polynomials with respect to a measure having a discrete real support. We also discuss the case of extremal polynomials wi th 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 t o discrete complex sets, such as the weighted discrete transfinite diameter and a weighted discrete Bernstein-Walsh-like inequality.