Jacobi matrices with absolutely continuous spectrum

Let J be a Jacobi matrix defined in l(2) as ReW, where W is a unilateral we ighted shift with nonzero weights lambda(k) such that lim(k) lambda(k) = 1. Define the seqences: epsilon(k) := lambda(k-1)/lambda(k) - 1, delta k := l ambda(k)-1/lambda(k), eta(k) := 2 delta(k) + epsilon(k). If epsilon(k) = O( k(-alpha)), eta(k) = O(k(-gamma)), 2/3 < alpha less than or equal to gamma, alpha + gamma > 3/2 and gamma > 3/4, then J has an absolutely continuous s pectrum covering (-2,2). Moreover, the asymptotics of the solution Ju = lam bda u, lambda is an element of R is also given.