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Duality theorems for slice hyperholomorphic functions
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Fabrizio Colombo
Published/Copyright:
August 11, 2010
Abstract
The aim of this paper is to provide a characterization of the dual of the ℝn-module of slice monogenic functions on a class of compact sets in the Euclidean space 
. 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 Köthe's theorem. The duality results are also obtained in the setting of quaternionic valued slice regular functions.
Received: 2008-10-20
Revised: 2009-03-31
Published Online: 2010-08-11
Published in Print: 2010-August
© Walter de Gruyter Berlin · New York 2010
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Articles in the same Issue
- La filtration de Harder-Narasimhan des schémas en groupes finis et plats
- Formules de caractères pour l'induction automorphe
- Duality theorems for slice hyperholomorphic functions
- Counting points of homogeneous varieties over finite fields
- Noncompact shrinking four solitons with nonnegative curvature
- Free analysis questions II: The Grassmannian completion and the series expansions at the origin
Articles in the same Issue
- La filtration de Harder-Narasimhan des schémas en groupes finis et plats
- Formules de caractères pour l'induction automorphe
- Duality theorems for slice hyperholomorphic functions
- Counting points of homogeneous varieties over finite fields
- Noncompact shrinking four solitons with nonnegative curvature
- Free analysis questions II: The Grassmannian completion and the series expansions at the origin
