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Advances in Applied Clifford Algebras

, Volume 18, Issue 2, pp 147–151 | Cite as

Hartogs Extension Theorem for Functions with Values in Complex Clifford Algebras

  • Ricardo Abreu BlayaEmail author
  • Juan Bory Reyes
Article
  • 48 Downloads

Abstract.

A regular extension phenomenon of functions defined on Euclidean space with values in a Clifford algebra was studied by Le Hung Son in the 90’s using methods of Clifford analysis, a function theory which, is centred around the notion of a monogenic function, i.e. a null solution of the firstorder, vector-valued Dirac operator in \({\mathbb{R}}^m\).

The isotonic Clifford analysis is a refinement of the latter, which arises for even dimension. As such it also may be regarded as an elegant generalization to complex Clifford algebra-valued functions of both holomorphic functions of several complex variables and two-sided biregular function theories.

The aim of this article is to present a Hartogs theorem on isotonic extendability of functions on a suitable domain of \({\mathbb{R}}^{2n}, n \geq 2\). As an application, the extension problem for holomorphic functions and so for the two-sided biregular ones is discussed.

Mathematics Subject Classification (2000).

Primary 30E20, 30E25 Secondary 30G20 

Keywords.

Hartogs extension theorem Clifford analysis 

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Copyright information

© Birkhauser 2008

Authors and Affiliations

  1. 1.Facultad de Informática y MatemáticaUniversidad de HolguínHolguínCuba
  2. 2.Departamento de MatemáticaUniversidad de OrienteSantiago de CubaCuba

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