2023/09/18 by Luis Miguel Anguas, Anguas, L. M., D. Barrios Rolanı́a +1
Mathematics · Physics and Astronomy · #15A23 #15B99 #33D45 #34L10 #39A70 #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2309.10059
openalex publication_date 2023/09/18 · openalex created_date 2023/09/21 · openalex updated_date 2026/08/01
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well as the corresponding eigenvalues. Also, some linear transformations are applied to sequences of eigenfunctions and a necessary condition for this to be a sequence of eigenfunctions of a new differential operator is obtained. These results are applied to the particular case of classical Hermite polynomials.