On classical orthogonal polynomials related to Hahn's operator. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Álvarez-Nodarse, R.; Castillo, K.; Mbouna, D.; Petronilho, J.
• Is Part Of: Integral transforms and special functions. Volume 31:Issue 6(2020)
• Page Start: 487
• Page End: 505
• Publication Date: 2020-06-02
• Subjects: Orthogonal polynomials -- moment linear functionals -- Hahn's operator -- regularity conditions; 42C05 -- 33C45; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2019.1702981
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: Let u be a non-zero linear functional acting on the space of polynomials. Let D q, ω be a Hahn operator acting on the dual space of polynomials. Suppose that there exist polynomials φ and ψ, with deg ⁡ φ ≤ 2 and deg ⁡ ψ ≤ 1, so that the functional equation D q, ω ( φ u ) = ψ u holds, where the involved operations are defined in a distributional sense. In this note we state necessary and sufficient conditions, involving only the coefficients of φ and ψ, such that u is regular, that is, there exists a sequence of orthogonal polynomials with respect to u .