Fischer decomposition by inframonogenic functions

• Helmuth R Malonek ^[2] ; Dixan Peña Peña ^[2] ; Frank Sommen ^[1]
  1. [1] Ghent University

     Ghent University

     Arrondissement Gent, Bélgica

     
  2. [2] Aveiro University Department of Mathematics
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 2, 2010, págs. 189-197
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000200012
• Enlaces
  • Texto completo
• Resumen
  • español

    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 δx fδx = 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.

  • English

    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.

• Referencias bibliográficas
  • Bock, S,Gürlebeck, K. (2009). On a spatial generalization of the Kolosov-Muskhelishvili formulae. Math. Methods Appl. Sci. 32. 223-240
  • Brackx, F. (1976). On (k)-monogenic functions of a quaternion variable. Funct. theor. Methods Differ. Equat. 22-44
  • Brackx, F. (1976). Non-(k)-monogenic points of functions of a quaternion variable. Funct. theor. Meth. part. Differ. Equat., Proc. int. Symp.,...
  • Brackx, F,Delanghe, R,Sommen, F. (1982). Clifford analysis. Pitman (Advanced Publishing Program. Boston, MA.
  • Cerejeiras, P,Sommen, F,Vieira, N. (2007). Fischer decomposition and special solutions for the parabolic Dirac operator, Math. Methods Appl....
  • Clifford, W. K. (1878). Applications of Grassmann’s Extensive Algebra. Amer. J. Math. 1. 350-358
  • De Bie, H,Sommen, F. (2008). Fischer decompositions in superspace: Function spaces in complex and Clifford analysis. Natl. Univ. Publ. Hanoi,...
  • Delanghe, R,Sommen, F,Soucek, V. (1992). Clifford algebra and spinor-valued functions. Kluwer Academic Publishers Group. Dordrecht.
  • Eelbode, D. (2007). Stirling numbers and spin-Euler polynomials. Experiment. Math. 16. 55-66
  • Faustino, N,Kähler, U. (2007). Fischer decomposition for difference Dirac operators. Adv. Appl. Clifford Algebr. 17. 37-58
  • Gürlebeck, K,Kähler, U. (1997). On a boundary value problem of the biharmonic equation. Math. Methods Appl. Sci. 20. 867-883
  • Malonek, H. R,Ren, G. (2002). Almansi-type theorems in Clifford analysis. Math. Methods Appl. Sci. 25. 1541-1552
  • Meleshko, V. V. (2003). Selected topics in the history of the two-dimensional biharmonic problem. Appl. Mech. Rev. 56. 33-85
  • Ren, G,Malonek, H. R. (2007). Almansi decomposition for Dunkl-Helmholtz operators, Wavelet analysis and applications. Appl. Numer. Harmon....
  • Ryan, J. (2000). Basic Clifford analysis. Cubo Mat. Educ. 2. 226-256
  • Sobrero, L. (1934). Theorie der ebenen Elastizität unter Benutzung eines Systems hyperkomplexerZahlen. Math. Einzelschriften. HamburgLeipzig....
  • Sommen, F. (1996). Monogenic functions of higher spin. Z. Anal. Anwendungen. 15. 279-282
  • Sommen, F,Van Acker, N. (1994). Functions of two vector variables. Adv. Appl. Clifford Algebr. 4. 65-72