Stability of Third Degree Linear Functionals and Rational Spectral Transformations

Salah, Imed Ben; Marcellán, Francisco; Khalfallah, Mohamed

doi:10.1007/s00009-022-02098-z

Cited by 1 publication

(2 citation statements)

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“…The third degree character is preserved by an affine transformation. Elementary transformations like association, perturbation, shift, multiplication and division by a polynomial, inversion, among others preserve the family of linear forms of third degree [6,10]. Furthermore, the class of third degree forms is closed under rational spectral transformations of the form [10].…”

Section: Definitionmentioning

confidence: 99%

“…Elementary transformations like association, perturbation, shift, multiplication and division by a polynomial, inversion, among others preserve the family of linear forms of third degree [6,10]. Furthermore, the class of third degree forms is closed under rational spectral transformations of the form [10]. In particular, we have Lemma 3 [6] Let u and v be two regular forms satisfying M (x)u = N (x)v, where M (x) and N (x) are two polynomials.…”

Section: Definitionmentioning

confidence: 99%

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Several characterizations of third degree semiclassical linear forms of class two appearing via cubic decomposition

Khalfallah

2022

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In this work we consider orthogonal polynomials via cubic decomposition in the framework of the third degree semiclassical class. Based on their third degree character, we give a complete description, by using the formal Stieltjes function and the moments, of semiclassical linear forms of class two arising from the cubic decomposition W3n(x) = Pn(x3); n ≥ 0. We focus our attention on the link between these forms and the strict third degree classical forms Vqk,l= J (k + q/3; l -q/3), q ∈{1,2},k,l ∈Z with k+ l≥ -1. All of them are rational transformations of the Jacobi form V = J (-2/3;-1=3).

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Section: Definitionmentioning

confidence: 99%