Weak classical orthogonal polynomials in two variables (Q1772341)

The paper contains 6 definitions, 3 lemmas, 4 propositions and 2 corollaries. The authors first introduce the concept of weak classical orthogonal polynomials in two variables. Next, three characterizations for weak classical orthogonal polynomials are established: the orthogonality of the gradients; the structure relation; and the matrix Bochner-type second-order partial differential equation. Then, some consequences of the characterizations are given. At the end, as a special case, the Krall and Sheffer classical orthogonal polynomials in two variables are recorded.