Marcellán Español, Francisco JoséPetronilho, José2010-01-042010-01-041999Portugaliae Mathematica, 1999, vol. 56, n. 1, p. 81-1130032-5155https://hdl.handle.net/10016/626333 pages, no figures.-- MSC1991 code: Primary 42C05.MR#: MR1680116 (2000b:42021)Zbl#: Zbl 0936.42012Starting from a sequence $\{P_n\}_{n\geq 0}$ of monic polynomials orthogonal with respect to a linear functional ${\bf u}$, we find a linear functional ${\bf v}$ such that $\{Q_n\}_{\geq 0}$, with either $Q_{2n}(x)=P_n(T(x))$ or $Q_{2n+1}(x)=(x-a)\,P_n(T(x))$ where $T$ is a monic quadratic polynomial and $a\in\C$, is a sequence of monic orthogonal polynomials with respect to ${\bf v}$. In particular, we discuss the case when ${\bf u}$ and ${\bf v}$ are both positive definite linear functionals. Thus, we obtain a solution for an inverse problem which is a converse, for quadratic mappings, of one analyzed in [11].application/pdfeng© European Mathematical SocietyOrthogonal polynomialsRecurrence coefficientsPolynomial mappingsStieltjes functionsresearch articleMatemáticasopen access