Spectral Measures and Jacobi Matrices Related to Laguerre-Type Systems of Orthogonal Polynomials

This paper considers systems of Laguerre-type orthogonal polynomials for which the corresponding Jacobi matrices represent unbounded self-adjoint operators which are bounded above or below. Under appropriate assumptions on the coefficient sequences in the recursion formula, results are obtained on the uniform boundedness of the polynomials on bounded intervals, the absence of eigenvalues for the corresponding operator, and the absolute continuity of the measure of orthogonality. Date received: September 7, 1995. Date revised: April 17, 1996.