Complete orthonormal sets of polynomial solutions of the Riesz and Moisil-Teodorescu systems in \(\mathbb R^{3}\) (Q1960257)

The author constructs complete orthonormal sets of polynomial solutions of the well-known Riesz system. Starting from Fueter polynomials in the description of H. R. Malonek, the procedure of orthonormalization by Gram-Schmidt is numerical unstable and great time-consuming. As an alternative, a family of Appell homogeneous monogenic polynomials (solutions of the Riesz-system) is deduced. This system has much better numerical properties. A similar construction also works for the Moisil-Teodorescu system. Recently, such questions are in the focus of several authors and therefore intensively studied.