Cubic decomposition of a Laguerre–Hahn linear functional I
Francisco Marcellán
Universidad Carlos III de Madrid, Leganés, SpainMohamed Khalfallah
University of Monastir, Monastir, Tunisia
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Abstract
The aim of this contribution is to study orthogonal polynomials via cubic decomposition in the framework of the Laguerre–Hahn class. We consider two monic orthogonal polynomial sequences and , and we let and be, respectively, the corresponding regular linear functionals such that , . We prove that if either or is a Laguerre–Hahn linear functional, then so is the other one. Based on this result, we deduce a complete analysis of the class of the Laguerre–Hahn linear functional . More precisely, we show that , where is the class of . An illustrative example of class is analyzed.
Cite this article
Francisco Marcellán, Mohamed Khalfallah, Cubic decomposition of a Laguerre–Hahn linear functional I. Z. Anal. Anwend. (2024), published online first
DOI 10.4171/ZAA/1760