On semiclassical orthogonal polynomials via polynomial mappings II: sieved ultraspherical polynomials revisited (Preprint)

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Type: Preprint
National /International: International
Title: On semiclassical orthogonal polynomials via polynomial mappings II: sieved ultraspherical polynomials revisited
Publication Date: 2017-07-10
Authors: - Kenier Castillo
- M. N. de Jesus
- José Carlos Petronilho
Abstract: In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work we use this fact to derive in an unified way old and new properties concerning the sieved ultraspherical polynomials of the first and second kind introduced by W. Al-Salam, W. R. Allaway, and R. Askey, and subsequently studied by several authors. Our results are stated in the more general framework of orthogonality with respect to a quasi-definite (or regular) moment linear functional, not necessarily represented by a weight function or positive Borel measure. This allow us to derive infinitely many examples of semiclassical functionals such that the pair of polynomials appearing in each corresponding canonical Pearson-type distributional differential equation is non-admissible.
Institution: DMUC 17-36
Online version: http://www.mat.uc.pt...prints/eng_2017.html
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