Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients

Abstract

We study solutions of three-term recurrence relations whose $N$-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more. Namely, we find the constructive formula for the density of their orthogonality measure in terms of Tur\'an determinants and we determine their exact asymptotic behavior. We treat both bounded and unbounded cases in a uniform manner.