The algebras of difference operators associated to Krall-Charlier orthogonal polynomials (Q723766)

The paper investigates Krall-Charlier polynomials as eigenvectors (functions) of a higher order difference operator. The author precisely considers the algebra of all difference operators such that the Krall-Charlier polynomials appear as as eigenfunctions relative to specific eigenvalues. A characterization of the algebra of difference operators is provided based on the characteristics of the eigenvalues polynomials one. A sort of isomorphism is proved between the eigenvalues polynomials algebra and the difference operators one in some specific cases (non-degenerate). Such correspondence is extended for larger cases. The paper is completed by some explicit examples even in the degenerate case. Overall, the paper addresses a fascinating subject. The mathematical developments are clear. Some extensions may be addressed from the present one in more general contexts such as the Clifford framework.