On Exceptional Sets of Asymptotic Relations for General Orthogonal Polynomials Original Research Article

The n-th root asymptotic behavior of orthonormal polynomials qn(z) corresponding to an arbitrary measure in the complex plane is studied. In particular, the following theorems are established (here Ω denotes the outer domain of the support of the measure, and gΩ(z) is the Green function of Ω): THEOREM 1. limn → ∞|qn(z)|1/n≥ egΩ(z) everywhere in Ω.THEOREM 2. limn → ∞|qn(z)|1/n≥ 1 everywhere on ∂Ω outside the discrete spectrum of the measure.THEOREM 3. For arbitrary countable set of points {ak}∞k=1 ⊂ of C there is a measure for which[formula]and[formula]