About the (Hahn) classical character of 2-orthogonal solutions of two families of differential equations of third order

TL;DR

This paper investigates 2-orthogonal polynomial solutions to third-order differential operators, demonstrating that these solutions satisfy Hahn's property within two classes of such operators.

Contribution

It proves that 2-orthogonal polynomial solutions of certain third-order differential operators possess Hahn's property, expanding understanding of their structure and properties.

Findings

2-orthogonal polynomial solutions satisfy Hahn's property

Analysis of dual space elements of polynomial eigenfunctions

Identification of two classes of differential operators with this property

Abstract

Considering a differential operator of third order that does not increase the degree of polynomials, we analyse some properties of elements of the dual space of 2-orthogonal polynomial eigenfunctions. In two classes of such generic operator, we prove that a 2-orthogonal polynomial solution fulfils Hahn's property.