Spectral Transformations of the Laurent Biorthogonal Polynomials, II. Pastro Polynomials

摘要

We continue to study the simplest closure conditions for chains ofspectral transformations of the Laurent biorthogonal polynomials($LBP$). It is shown that the 1-1-periodic $q$-closure conditionleads to the $LBP$ introduced by Pastro. We introduce classes of semi-classical and Laguerre-Hahn $LBP$ associated to generic closure conditions of the chain of spectral transformations.