Complex Variables and Elliptic Equations vol:53 issue:3 pages:195-213
In this paper we deal with entire Clifford algebra valued
solutions to polynomial Cauchy-Riemann equations in higher
dimensional Euclidean spaces. We introduce generalizations of the maximum term and the central index within the context of this family of elliptic partial differential equations. These notions enable us to perform a basic study of the asymptotic growth behavior of entire solutions to these systems. In this paper we set up generalizations of some classical fundamental results of Wiman and Valiron's theory. Our results then enable us to get some insight on the structure of the solutions of a certain class of higher dimensional PDE.