This paper studies the spectral measure of an unbounded tridiagonal matrix operator for which the matrix entries satisfy a certain growth condition, and presents a sufficient condition for the existence of an absolutely continuous part. The results are related to a class of orthogonal polynomials with exponential weights.
(1988). Spectral Measures, Orthogonal Polynomials, and Absolute Continuity. SIAM Journal on Mathematical Analysis, 19 (4), 939-943.