Absolutely continuous measures for systems of orthogonal polynomials with unbounded recurrence coefficients (Q1185194)

An important problem in the theory of orthogonal polynomials is to obtain information on the orthogonality measure when the coefficients in the three-term recurrence relation for the orthogonal polynomials are known. When the recurrence coefficients are bounded, then general results for bounded self-adjoint operators can be applied to the Jacobi matrix, and these lead to useful results. This paper shows how one can deal with unbounded recurrence coefficients. The author uses commutator equations for the (unbounded) Jacobi operator to find a large class of unbounded recurrence coefficients for which the orthogonality measure is absolutely continuous.