TY - JOUR
T1 - Solutions of Inhomogeneous Generalized Moisil–Teodorescu Systems in Euclidean Space
AU - Bory-Reyes, Juan
AU - Pérez-de la Rosa, Marco Antonio
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - Let R0,m+1(s) be the space of s-vectors (0 ≤ s≤ m+ 1) in the Clifford algebra R , m + 1 constructed over the quadratic vector space R , m + 1 , let r, p, q∈ N with 0 ≤ r≤ m+ 1 , 0 ≤ p≤ q and r+ 2 q≤ m+ 1 and let R0,m+1(r,p,q)=∑j=pq⨁R0,m+1(r+2j). Then a R0,m+1(r,p,q)-valued smooth function F defined in an open subset Ω ⊂ R m + 1 is said to satisfy the generalized Moisil–Teodorescu system of type (r, p, q) if ∂ x F= 0 in Ω , where ∂ x is the Dirac operator in R m + 1 . To deal with the inhomogeneous generalized Moisil–Teodorescu systems ∂ x F= G, with a ∑j=pq⨁R0,m+1(r+2j-1)-valued continuous function G as a right-hand side, we embed the systems in an appropriate Clifford analysis setting. Necessary and sufficient conditions for the solvability of inhomogeneous systems are provided and its general solution described.
AB - Let R0,m+1(s) be the space of s-vectors (0 ≤ s≤ m+ 1) in the Clifford algebra R , m + 1 constructed over the quadratic vector space R , m + 1 , let r, p, q∈ N with 0 ≤ r≤ m+ 1 , 0 ≤ p≤ q and r+ 2 q≤ m+ 1 and let R0,m+1(r,p,q)=∑j=pq⨁R0,m+1(r+2j). Then a R0,m+1(r,p,q)-valued smooth function F defined in an open subset Ω ⊂ R m + 1 is said to satisfy the generalized Moisil–Teodorescu system of type (r, p, q) if ∂ x F= 0 in Ω , where ∂ x is the Dirac operator in R m + 1 . To deal with the inhomogeneous generalized Moisil–Teodorescu systems ∂ x F= G, with a ∑j=pq⨁R0,m+1(r+2j-1)-valued continuous function G as a right-hand side, we embed the systems in an appropriate Clifford analysis setting. Necessary and sufficient conditions for the solvability of inhomogeneous systems are provided and its general solution described.
KW - Clifford analysis
KW - Conjugate harmonic pairs
KW - Dirac operator
KW - Moisil–Teodorescu systems
UR - http://www.scopus.com/inward/record.url?scp=85061674344&partnerID=8YFLogxK
U2 - 10.1007/s00006-019-0946-3
DO - 10.1007/s00006-019-0946-3
M3 - Artículo
SN - 0188-7009
VL - 29
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 2
M1 - 27
ER -