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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.2 Temuco  2010 

CUBO A Mathematical Journal Vol.12, N° 02, (189-197). June 2010


Fischer decomposition by inframonogenic functions


Helmuth R. Malonek1, Dixan Peña Peña2 and Frank Sommen

Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal 1email: 2 email:,

Department of Mathematical Analysis, Ghent University, 9000 Gent, Belgium email:


Let δx denote the Dirac operator in Rm. In this paper, we present a refinement of the biharmonic functions and at the same time an extension of the monogenic functions by considering the equation δxf δx = 0. The solutions of this “sandwich” equation, which we call inframonogenic functions, are used to obtain a new Fischer decomposition for homogeneous polynomials in Rm.

Key words and phrases: Inframonogenic functions; Fischer decomposition.


Denotemos por δx el operador de Dirac en Rm. En este artículo, nosotros presentamos un refinamiento de las funciones biarmónicas y al mismo tiempo una extensión de las funciones monogénicas considerando la ecuación δxx = 0. Las soluciones de esta ecuación tipo “sándwich”, las cuales llamaremos inframonogénicas, son utilizadas para obtener una nueva descomposición de Fischer para polinomios homogéneos en Rm.

Mathematics Subject Classification: 30G35; 31B30; 35G05.


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Received: March 2009.

Revised: May 2009.