Monogenic functions of higher spin by cauchy-kovalevska extension of real-analytic functions

Abstract

In this paper we will present necessary and sufficient conditions for a real-analytic function to have a Cauchy-Kovalevska extension monogenic of higher spin and show how these conditions are similar to the hypothesis in a generalized version of Poincare's lemma. This leads to a local characterization of monogenic functions of higher spin.

Keywords:

• Monogenic functions
• Cauchy Kovaleska
• Clifford algebra

AMS No:

• 30G35

^†Supported by Centro de Matemática da Universidade de Coimbrs, FCT/PRAXIS XXI and RUG.

^†Supported by Centro de Matemática da Universidade de Coimbrs, FCT/PRAXIS XXI and RUG.

Notes

^†Supported by Centro de Matemática da Universidade de Coimbrs, FCT/PRAXIS XXI and RUG.