Fischer decomposition by inframonogenic functions

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DOI:

https://doi.org/10.4067/S0719-06462010000200012

Abstract

Let ∂x denote the Dirac operator in â„m. 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 ∂xf∂x = 0. The solutions of this “sandwich” equation, which we call inframonogenic functions, are used to obtain a new Fischer decomposition for homogeneous polynomials in â„m.

Keywords

Inframonogenic functions , Fischer decomposition
  • Helmuth R. Malonek Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal.
  • Dixan Peña Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal.
  • Frank Sommen Department of Mathematical Analysis, Ghent University, 9000 Gent, Belgium.
  • Pages: 189–197
  • Date Published: 2010-06-01
  • Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal

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Published

2010-06-01

How to Cite

[1]
H. R. Malonek, D. Peña, and F. Sommen, “Fischer decomposition by inframonogenic functions”, CUBO, vol. 12, no. 2, pp. 189–197, Jun. 2010.

Issue

Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal

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