dc.creatorDelanghe,Richard
dc.date2010-01-01
dc.date.accessioned2017-03-07T16:36:24Z
dc.date.available2017-03-07T16:36:24Z
dc.identifierhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000200010
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/404494
dc.descriptionLet for s &#8712; {0, 1, ...,m+ 1} (m &#8805; 2) , IR(s)0,m+1 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, &#8712; IN be such that 0 &#8804; r &#8804; m + 1, p < q and r + 2q &#8804; m + 1. The associated linear system of first order partial differential equations derived from the equation &#8706;xW = 0 where W is IR(r,p,q)0,m+1 = &#8721;q j=p &#8853;IR(r+2j)0,m+1 -valued and &#8706;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 &#8712; N, k &#8805; 1,MT+(m+ 1; k; IR(r,p,q)0,m+1), denotes the space of IR(r,p,q)0,m+1-valued homogeneous polynomials Wc of degree k in IRm+1 satisfying &#8706;xWx = 0. A characterization of Wk&#8712; MT+(m + 1; k;IR(r,p,q)0,m+1) is given in terms of a harmonic potential Hk+1 belonging to a subclass of IR(r,p,q)0,m -valued solid harmonics of degree (k + 1) in IRm+1. Furthermore, it is proved that each Wk&#8712; MT+(m+ 1; k; IR(r,p,q)0,m+1) admits a primitive Wk+1 &#8712; MT+(m+ 1; k + 1; IR(r,p,q)0,m+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 MT+(4; k; IR(r,p,q)0,4), r being even.
dc.formattext/html
dc.languageen
dc.publisherUniversidad de La Frontera. Departamento de Matemática y Estadística
dc.publisherUniversidade Federal de Pernambuco. Departamento de Matemática
dc.sourceCubo (Temuco) v.12 n.2 2010
dc.subjectClifford analysis
dc.subjectMoisil-Théodoresco systems
dc.subjectconjugate harmonic funtions
dc.subjectharmonic potentials
dc.subjectpolynomial bases
dc.titleOn homogeneous polynomial solutions of generalized Moisil-Théodoresco systems in Euclidean space
dc.typeArtículos de revistas


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