A Generalization of Wiman and Valiron‘s theory to the Clifford analysis setting

Abstract

The classical notions of growth orders, maximum term and the central index provide powerful tools to study the asymptotic growth behavior of complex-analytic functions. This leads to much insight into the structure of the solutions to many two dimensional partial differential equations that are related to boundary value problems from harmonic analysis in the plane. In this overview paper we show how the classical techniques and results from Wiman and Valiron can be extended to the Clifford analysis setting in order to treat successfully analogous higher dimensional problems.