Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions
Joint Authors
Sommen, Frank
Abreu Blaya, Ricardo
Delanghe, Richard
Bory Reyes, Juan
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-03-17
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
Let ℝ0,m+1(s) be the space of s-vectors (0≤s≤m+1) in the Clifford algebra ℝ0,m+1 constructed over the quadratic vector space ℝ0,m+1, let r,p,q∈ℕ with 0≤r≤m+1, 0≤p≤q, and r+2q≤m+1, and let ℝ0,m+1(r,p,q)=∑j=pq⨁ℝ0,m+1(r+2j).
Then, an ℝ0,m+1(r,p,q)-valued smooth function W defined in an open subset Ω⊂ℝm+1 is said to satisfy the generalized Moisil-Théodoresco system of type (r,p,q) if ∂xW=0 in Ω, where ∂x is the Dirac operator in ℝm+1.
A structure theorem is proved for such functions, based on the construction of conjugate harmonic pairs.
Furthermore, if Ω is bounded with boundary Γ, where Γ is an Ahlfors-David regular surface, and if W is a ℝ0,m+1(r,p,q)-valued Hölder continuous function on Γ, then necessary and sufficient conditions are given under which W admits on Γ a Cauchy integral decomposition W=W++W−.
American Psychological Association (APA)
Abreu Blaya, Ricardo& Bory Reyes, Juan& Delanghe, Richard& Sommen, Frank. 2008. Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions. International Journal of Mathematics and Mathematical Sciences،Vol. 2008, no. 2008, pp.1-19.
https://search.emarefa.net/detail/BIM-987904
Modern Language Association (MLA)
Abreu Blaya, Ricardo…[et al.]. Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions. International Journal of Mathematics and Mathematical Sciences No. 2008 (2008), pp.1-19.
https://search.emarefa.net/detail/BIM-987904
American Medical Association (AMA)
Abreu Blaya, Ricardo& Bory Reyes, Juan& Delanghe, Richard& Sommen, Frank. Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions. International Journal of Mathematics and Mathematical Sciences. 2008. Vol. 2008, no. 2008, pp.1-19.
https://search.emarefa.net/detail/BIM-987904
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-987904