SPECTRAL MEASURES AND JACOBI MATRICES RELATED TO LAGUERRE-TYPE SYSTEMS OF ORTHOGONAL POLYNOMIALS

This paper considers systems of Laguerre-type orthogonal polynomials f or which the corresponding Jacobi matrices represent unbounded self-ad joint operators which are bounded above or below. Under appropriate as sumptions on the coefficient sequences in the recursion formula, resul ts are obtained on the uniform boundedness of the polynomials on bound ed intervals, the absence of eigenvalues for the corresponding operato r, and the absolute continuity of the measure of orthogonality.