On the solutions of a class of iterated generalized Bers–Vekua equations in Clifford analysis

We consider functions with values in the Clifford algebra Cl p,q which are solutions of a certain class of the iterated generalized Bers–Vekua equation D m w =0 with Dw = ∂ w + c w̄ where \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}$\partial={\sum\nolimits_{j=0}^{n}}e_j\,\partial/{\partial x_j}$\end{document} is the generalized Cauchy–Riemann operator and x = x 0 + x 1 e 1 +… x n e n . We prove that any such function w has an Almansi‐type decomposition of the form w = v 0 + x 0 v 1 +···+ x   m− 1 0v m− 1 where the functions v j , j =0,1,…, m− 1, are solutions of the generalized Bers–Vekua equation Dv =0. Copyright © 2009 John Wiley & Sons, Ltd.