Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations

Symmetry Integrability and Geometry-Methods and Applications

article

Clotilde Martínez¹  Miguel A. Piñar¹ 

[1] Universidad de Granada

关键词: multivariate orthogonal polynomials;    unit ball;    partial dif ferential equations;   

DOI  :  10.3842/SIGMA.2016.020

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown