Matrix Pearson equations satisfied by Koornwinder weights in two variables (Q683653)

The authors consider bivariate Koornwinder weight functions constructed from semi-classical univariate weights. As it was proven in [\textit{L. Fernández} et al., J. Comput. Appl. Math. 236, No. 15, 3817--3826 (2012; Zbl 1262.42007)], these weight functions satisfy a certain matrix partial differential equation, but the coefficients are not polynomials in general. This paper gives two symmetrization methods to guarantee a regular matrix Pearson equation with matrix polynomial coefficients. The authors also study some examples and derive second-order partial differential operators associated with semiclassical Koornwinder polynomials.