Asymptotics for orthogonal polynomials on and off the essential spectrum

AbstractWe assume that the coefficients in the three term recurrence relation for orthogonal polynomials form sequences of bounded variation and we show that the asymptotic behavior of the orthogonal polynomials on the essential spectrum is closely related to the asymptotic behavior in the complex plane (off the essential spectrum), proving a conjecture of Máté, Nevai and Totik [Constr. Approx. 1 (1985), 231–248]