TY - JOUR
T1 - Harmonic multivector fields and the Cauchy integral decomposition in Clifford analysis
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Sommen, Frank
AU - Delanghe, Richard
PY - 2004
Y1 - 2004
N2 - In this paper we study the problem of decomposing a Hölder continuous k-grade multivector field Fk on the boundary Γ of an open bounded subset Ω in Euclidean space ℝn into a sum F k = Fk+ + Fk- of harmonic k-grade multivector fields Fk± in Ω+ = Ω and Ω- = ℝn / (Ω ∪ Γ) respectively. The necessary and sufficient conditions upon Fk we thus obtain complement those proved by Dyn'kin in [20,21] in the case where Fk is a continuous k-form on Γ. Being obtained within the framework of Clifford analysis and hence being of a pure function theoretic nature, they once more illustrate the importance of the interplay between Clifford analysis and classical real harmonic analysis.
AB - In this paper we study the problem of decomposing a Hölder continuous k-grade multivector field Fk on the boundary Γ of an open bounded subset Ω in Euclidean space ℝn into a sum F k = Fk+ + Fk- of harmonic k-grade multivector fields Fk± in Ω+ = Ω and Ω- = ℝn / (Ω ∪ Γ) respectively. The necessary and sufficient conditions upon Fk we thus obtain complement those proved by Dyn'kin in [20,21] in the case where Fk is a continuous k-form on Γ. Being obtained within the framework of Clifford analysis and hence being of a pure function theoretic nature, they once more illustrate the importance of the interplay between Clifford analysis and classical real harmonic analysis.
KW - Cauchy transform
KW - Clifford analysis
KW - Multivector fields
UR - http://www.scopus.com/inward/record.url?scp=2442509684&partnerID=8YFLogxK
U2 - 10.36045/bbms/1080056163
DO - 10.36045/bbms/1080056163
M3 - Artículo
SN - 1370-1444
VL - 11
SP - 95
EP - 110
JO - Bulletin of the Belgian Mathematical Society - Simon Stevin
JF - Bulletin of the Belgian Mathematical Society - Simon Stevin
IS - 1
ER -