Cubic decomposition of a Laguerre–Hahn linear functional I

  • Francisco Marcellán

    Universidad Carlos III de Madrid, Leganés, Spain
  • Mohamed Khalfallah

    University of Monastir, Monastir, Tunisia
Cubic decomposition of a Laguerre–Hahn  linear functional I cover
Download PDF

This article is published open access under our Subscribe to Open model.

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. 43 (2024), no. 3/4, pp. 471–510

DOI 10.4171/ZAA/1760