Recurrence Coefficients of Orthogonal Polynomials with Respect to Some Self-Similar Singular Distributions

Abstract

The limiting behaviour of arithmetic and geometric means of the coefficients of three term recurrence relations satisfied by orthogonal polynomials is investigated. The measure of orthogonality is not assumed to be absolutely continuous, but it must guarantee regular limit distribution of the zeros of the orthogonal polynomials. Some examples of self-similar distributions satisfying this condition are given.