Spectral transformations and second kind polynomials associated with a hermitian linear functional

The aim of this paper is to analyze the relation between the Christoffel transformations in the framework of hermitian linear functionals and the associated polynomials of the second kind through of their associated Carathéodory formal power series. In particular, some results are given in the way of characterization of linear spectral transformations using Christoffel and Geronimus transformations. This gives a new example of rational spectral transformation that has not yet been studied in the literature.