Bounds on orthogonal polynomials and separation of their zeros

Let ${ p\_{n}}$ denote the orthonormal polynomials associated with a measure $\mu$ compact support on real line. be regular in sense of Stahl, Totik, and Ullmann, $I$ subinterval which is absolutely continuous, while $\mu'$ positive continuous there. We show that boundedness $% { closely related to spacing zeros $p\_{n}$ $p\_{n-1}$ interval. One ingredient proving “local limits” imply universality limits.