Spectra of rational orthonormal systems

We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions in the Laguerre and the Kautz systems are the eigenvectors of modified Sturm-Liouville operators. The results are further generalized to multiple parameters of one complex variable in both the unit disc and the upper half-plane contexts.