Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions
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⊂ℝ...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/746946 |
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| author | Ricardo Abreu Blaya Juan Bory Reyes Richard Delanghe Frank Sommen |
| author_facet | Ricardo Abreu Blaya Juan Bory Reyes Richard Delanghe Frank Sommen |
| author_sort | Ricardo Abreu Blaya |
| collection | DOAJ |
| description | 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−. |
| format | Article |
| id | doaj-art-842abefcab0340c4a7b6a96f4e66ed33 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-842abefcab0340c4a7b6a96f4e66ed332025-02-03T06:44:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/746946746946Generalized Moisil-Théodoresco Systems and Cauchy Integral DecompositionsRicardo Abreu Blaya0Juan Bory Reyes1Richard Delanghe2Frank Sommen3Facultad de Informática y Matemática, Universidad de Holguín, Holguín 80100, CubaDepartamento de Matemática, Facultad de Matemática y Computación, Universidad de Oriente, Santiago de Cuba 90500, CubaDepartment of Mathematical Analysis, Ghent University, 9000 Ghent, BelgiumDepartment of Mathematical Analysis, Ghent University, 9000 Ghent, BelgiumLet 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−.http://dx.doi.org/10.1155/2008/746946 |
| spellingShingle | Ricardo Abreu Blaya Juan Bory Reyes Richard Delanghe Frank Sommen Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions International Journal of Mathematics and Mathematical Sciences |
| title | Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions |
| title_full | Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions |
| title_fullStr | Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions |
| title_full_unstemmed | Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions |
| title_short | Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions |
| title_sort | generalized moisil theodoresco systems and cauchy integral decompositions |
| url | http://dx.doi.org/10.1155/2008/746946 |
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