Duality theorems for slice hyperholomorphic functions

The aim of this paper is to provide a characterization of the dual of the R_n-module of slice monogenic functions on a class of compact sets in the Euclidean space R^{n+1}. Despite the fact that the Cauchy formulas which are essential to such a characterization are based on different kernels, depending on whether one considers right or left slice monogenic functions, we are still able to establish a duality theorem which, since holomorphic functions are a very special case of slice monogenic functions, is the generalization of Kothe's theorem. The duality results are also obtained in the setting of quaternionic valued slice regular functions.