In the paper we represent two examples which are based on the properties of discrete measures. In the first part of the paper we prove that for each probability measure μ, suppμ = [−1, 1], which logarithmic potential is a continuous function on [−1, 1] there exists a (discrete) measure σ = σ(μ), suppσ = [−1, 1], with the following property. Let {Pn(x;σ)} be the sequence of polynomials orthogonal with respect to σ. Then 1 n χ(Pn(·; σ)) ∗ → μ, n → ∞, where χ(·) is zero counting measure for the… Expand

In the paper, we discuss how it would be possible to succeed in Stahl’s novel approach, 1987–1988, to explore Hermite–Padé polynomials based on Riemann surface properties. In particular, we explore… Expand

This treatment of potential theory emphasizes the effects of an external field (or weight) on the minimum energy problem. Several important aspects of the external field problem (and its extension to… Expand

Let be a positive measure on the circumference and let almost everywhere on . Let be the orthogonal polynomials corresponding to , and let be their parameters. Then .Bibliography: 5 titles.