dc.creator | Delanghe, Richard | |
dc.date | 2010-06-01 | |
dc.identifier | https://revistas.ufro.cl/ojs/index.php/cubo/article/view/1412 | |
dc.identifier | 10.4067/S0719-06462010000200010 | |
dc.description | Let for s ∈ {0, 1, ..., m + 1} (m ≥ 2), be the space of s-vectors in the Clifford algebra IR0,m+1 constructed over the quadratic vector space IR0,m+1 and let r, p, q, ∈ IN be such that 0 ≤ r ≤ m + 1, p < q and r + 2q ≤ m + 1. The associated linear system of first order partial differential equations derived from the equation ∂xW = 0 where W is -valued and ∂x is the Dirac operator in IRm+1, is called a generalized Moisil-Théodoresco system of type (r, p, q) in IRm+1. For k ∈ N, k ≥ 1, , denotes the space of -valued homogeneous polynomials Wk of degree k in IRm+1 satisfying ∂xWk = 0. A characterization of Wk ∈ is given in terms of a harmonic potential Hk+1 belonging to a subclass of -valued solid harmonics of degree (k + 1) in IRm+1. Furthermore, it is proved that each Wk ∈ admits a primitive Wk+1 ∈ . Special attention is paid to the lower dimensional cases IR3 and IR4. In particular, a method is developed for constructing bases for the spaces , r being even. | en-US |
dc.format | application/pdf | |
dc.language | eng | |
dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
dc.relation | https://revistas.ufro.cl/ojs/index.php/cubo/article/view/1412/1277 | |
dc.source | CUBO, A Mathematical Journal; Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal; 145–167 | en-US |
dc.source | CUBO, A Mathematical Journal; Vol. 12 Núm. 2 (2010): CUBO, A Mathematical Journal; 145–167 | es-ES |
dc.source | 0719-0646 | |
dc.source | 0716-7776 | |
dc.subject | Clifford analysis | en-US |
dc.subject | Moisil-Théodoresco systems | en-US |
dc.subject | conjugate harmonic funtions | en-US |
dc.subject | harmonic potentials | en-US |
dc.subject | polynomial bases | en-US |
dc.title | On homogeneous polynomial solutions of generalized Moisil-Théodoresco systems in Euclidean space | en-US |
dc.type | info:eu-repo/semantics/article | |
dc.type | info:eu-repo/semantics/publishedVersion | |