  We consider Koornwinder's method for constructing orthogonal polynomials in
two variables from orthogonal polynomials in one variable. If semiclassical
orthogonal polynomials in one variable are used, then Koornwinder's
construction generates semiclassical orthogonal polynomials in two variables.
We consider two methods for deducing matrix Pearson equations for weight
functions associated with these polynomials, and consequently, we deduce the
second order linear partial differential operators for classical Koornwinder
polynomials.
