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.
Duality theorems for slice hyperholomorphic functions
COLOMBO, FABRIZIO;SABADINI, IRENE MARIA;
2010-01-01
Abstract
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.File | Dimensione | Formato | |
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