TY - JOUR
T1 - On the structure of solutions of the Moisil-Théodoresco system in euclidean space
AU - Reyes, Juan Bory
AU - Delanghe, Richard
N1 - Funding Information:
(1) This paper was written while the first author was visiting the Department of Mathematical Analysis of Ghent University. He was supported by the Special Research Fund No. 01T13804 of Ghent University obtained for collabora-tion between the Clifford Research Group in Ghent and the Cuban Research Group in Clifford analysis, on the subject Boundary value theory in Clifford Analysis. Juan Bory Reyes wishes to thank the members of this Department for their kind hospitality.
PY - 2009/2
Y1 - 2009/2
N2 - Let Ω ⊂ ℝm+1 be open, let ∂ x be the Dirac operator in ℝm+1 and let ℝ0, m+1 be the Clifford algebra constructed over the quadratic space ℝ0, m+1. If for r ∈ {0, 1, ?., m} fixed, ℝ(r)0, m+1 denotes the space of r-vectors in ℝ0, m+1, then an Rdbl;r 0,m+1 ⊕ ℝ (r+2)0,m+1 -valued smooth function W = W r + W r+2 in Ω is said to satisfy the Moisil-Théodoresco system if ∂xW = 0{rm in},Ω. In terms of differential forms, this means that the corresponding (r (Ω) ⊕ r+2(Ω)) - valued smooth form w = w r + w r+2 satisfies in Ω the system d * w r = 0, dw r + d * w r+2 = 0; dw r+2 = 0. Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure theorem is proved for the solutions of the Moisil-Théodoresco system.
AB - Let Ω ⊂ ℝm+1 be open, let ∂ x be the Dirac operator in ℝm+1 and let ℝ0, m+1 be the Clifford algebra constructed over the quadratic space ℝ0, m+1. If for r ∈ {0, 1, ?., m} fixed, ℝ(r)0, m+1 denotes the space of r-vectors in ℝ0, m+1, then an Rdbl;r 0,m+1 ⊕ ℝ (r+2)0,m+1 -valued smooth function W = W r + W r+2 in Ω is said to satisfy the Moisil-Théodoresco system if ∂xW = 0{rm in},Ω. In terms of differential forms, this means that the corresponding (r (Ω) ⊕ r+2(Ω)) - valued smooth form w = w r + w r+2 satisfies in Ω the system d * w r = 0, dw r + d * w r+2 = 0; dw r+2 = 0. Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure theorem is proved for the solutions of the Moisil-Théodoresco system.
KW - Conjugate harmonic pairs
KW - Moisil-Théodoresco system
KW - Monogenic functions
KW - Self-conjugate differential forms
UR - http://www.scopus.com/inward/record.url?scp=59449095905&partnerID=8YFLogxK
U2 - 10.1007/s00006-008-0121-8
DO - 10.1007/s00006-008-0121-8
M3 - Artículo
AN - SCOPUS:59449095905
SN - 0188-7009
VL - 19
SP - 15
EP - 28
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 1
ER -