Hartogs extension theorem for functions with values in complex clifford algebras

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 ℝm. 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 ℝ2n, n ≥ 2. As an application, the extension problem for holomorphic functions and so for the two-sided biregular ones is discussed. © 2008 Birkhauser Verlag Basel/Switzerland.

Año de publicación:

2008

Keywords:

• Hartogs extension theorem
• Clifford analysis

Fuente:

scopus