Stability of Third Degree Linear Functionals and Rational Spectral Transformations

In this paper, we consider linear forms of the third degree class. This means that the Stieltjes function associated with the corresponding moment sequence satisfies a cubic equation with polynomial coefficients. We introduce the notion of a primitive triple of a strict third degree form. A simplification criterion of the corresponding cubic algebraic equation is given. Moreover, we show that the class of third degree linear forms is closed under rational spectral transformations. Several consequences of this fact are deduced. In particular, we illustrate with several examples the set of third degree linear forms is stable for the most standard algebraic operations in the linear space of linear forms.

associated forms; orthogonal polynomials; perturbed forms; rational spectral transformations; stieltjes function; third degree forms

Stability of Third Degree Linear Functionals and Rational Spectral Transformations Articles