This manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study and characterization of the classical families, namely Hermite, Laguerre, Jacobi, and Bessel polynomials. It is presented a cyclical proof of some of the most relevant characterizations, particularly those due to Al-Salam and Chihara, Bochner, Hahn, Maroni, and McCarthy. Two apparently new characterizations are also added. Moreover, it is proved… Expand

Given two polynomials φ and ψ such that deg φ ≤ 2 and deg ψ = 1, and a continuous linear functional U (defined on the space of all polynomials with complex coefficients) which is a solution of the… Expand

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

Les fonctions euleriennes ont une situation particuliere : elles apparaissent dans presque toutes les questions touchant les autres fonctions speciales, c’est‐a‐dire qu’elles interviennent, en… Expand