On Koornwinder classical orthogonal polynomials in two variables

摘要

In 1975, Tom Koornwinder studied examples of two variable analogues of the Jacobi polynomials in two variables. Those orthogonal polynomials are eigenfunctions of two commuting and algebraically independent partial differential operators. Some of these examples are well known classical orthogonal polynomials in two variables, such as orthogonal polynomials on the unit ball, on the simplex or the tensor product of Jacobi polynomials in one variable, but the remaining cases are not considered classical by other authors. The definition of classical orthogonal polynomials considered in this work provides a different perspective on the subject. We analyze in detail Koornwinder polynomials and using the Koornwinder tools, new examples of orthogonal polynomials in two variables are given.