On some constructive aspects of monogenic function theory in ℝ4

As is well known, a possible generalization to ℝ4 of the classical Cauchy–Riemann system leads to the so‐called Riesz system. The main goal of this paper is to construct explicitly a complete orthonormal system of polynomial solutions of this system with respect to a certain inner product. This will be done in the spaces of square integrable functions on the unit ball over ℝ. Copyright © 2011 John Wiley & Sons, Ltd.