An inverse problem associated with (1,1) symmetric coherent linear functionals

Abstract

ABSTRACTIn this paper we study an inverse problem associated with the non-coherent algebraic relation where the sequences of monic polynomials and are orthogonal with respect to quasi-definite linear functionals u, v and w, respectively, and for We assume that v is a monic polynomial perturbation of u. Moreover, in the case we assume that u is a semiclassical linear functional of class s. In this way, we discuss the relation between the formal Stieltjes series associated with u and w. This inverse problem is motivated by the analysis of sequences of polynomials orthogonal with respect to symmetric coherent pairs of linear functionals when a symmetrization process is implemented.