Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations
Classical Analysis and ODEs
2016-02-24 v2
Abstract
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of orthogonal polynomials. Then, using the representation of these polynomials in terms of spherical harmonics, algebraic and differential properties will be deduced.
Keywords
Cite
@article{arxiv.1511.07056,
title = {Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations},
author = {Clotilde Martínez and Miguel A. Piñar},
journal= {arXiv preprint arXiv:1511.07056},
year = {2016}
}