Monomial and Rodrigues orthogonal polynomials on the cone


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AKTAŞ R., Branquinho A., Foulquié-Moreno A., Xu Y.

Journal of Mathematical Analysis and Applications, vol.522, no.2, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 522 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1016/j.jmaa.2022.126977
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Cones, Laguerre and Jacobi, Monomial polynomials, Orthogonal polynomials, Rodrigues formula
  • Ankara University Affiliated: Yes

Abstract

© 2022 Elsevier Inc.We study two families of orthogonal polynomials with respect to the weight function [Formula presented], [Formula presented], on the cone {(x,t):‖x‖≤t,x∈Rd,t>0} in Rd+1. The first family consists of monomial polynomials Vk,n(x,t)=tn−|k|xk+⋯ for k∈N0d with |k|≤n, which has the least L2 norm among all polynomials of the form tn−|k|xk+P with deg⁡P≤n−1, and we will provide an explicit construction for Vk,n. The second family consists of orthogonal polynomials defined by the Rodrigues type formulas when w is either the Laguerre weight or the Jacobi weight, which satisfies a generating function in both cases. The two families of polynomials are partially biorthogonal.