Monomial and Rodrigues orthogonal polynomials on the cone

Creative Commons License

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

Journal of Mathematical Analysis and Applications, cilt.522, sa.2, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 522 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.jmaa.2022.126977
  • Dergi Adı: Journal of Mathematical Analysis and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Orthogonal polynomials, Cones, Monomial polynomials, Rodrigues formula, Laguerre and Jacobi, FORMULA
  • Ankara Üniversitesi Adresli: Evet

Özet

© 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.