Cubic decomposition of a Laguerre-Hahn linear functional I (Q6621592)

Consider two sequences of monic orthogonal polynomials \(\{W_n\}_{n\geq 0}\) and \(\{P_n\}_{n\geq 0}\) and let \(w\) and \(u\) be, respectively, the corresponding regular linear functionals such that \(W_{2n}(x)=P_n(x^3),\) \(n\geq 0.\) The authors prove that \(w\) is a Laguerre-Hahn linear functional if and only if \(u\) is a Laguerre-Hahn linear functional.