TY - JOUR
T1 - Hartogs extension theorem for functions with values in complex clifford algebras
AU - Blaya, Ricardo Abreu
AU - Reyes, Juan Bory
N1 - Funding Information:
The authors wish to thank the IMPA, Rio de Janeiro, where the paper was written, for the invitation and hospitality. They were partially supported by the CAPES-MES project 028/07.
PY - 2008/5
Y1 - 2008/5
N2 - 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.
AB - 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.
KW - Clifford analysis
KW - Hartogs extension theorem
UR - http://www.scopus.com/inward/record.url?scp=43649096447&partnerID=8YFLogxK
U2 - 10.1007/s00006-008-0064-0
DO - 10.1007/s00006-008-0064-0
M3 - Artículo
AN - SCOPUS:43649096447
SN - 0188-7009
VL - 18
SP - 147
EP - 151
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 2
ER -