Second kind functionals for the Laguerre-Hahn affine class on the unit circle

Abstract

The aim of this paper is the study of some transformations in the Laguerre-Hahn affine class that do not preserve the class. Under very general conditions, we establish that the second kind functional associated with a Laguerre-Hahn affine functional does not belong to the Laguerre-Hahn affine class. The transformations related to the associated polynomials and quadratic decomposition of a sequence of orthogonal polynomials are also considered.