Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/22094
Title: Hypermonogenic functions of two vector variables
Author: Eriksson, S.-L.
Orelma, H.
Vieira, Nelson Felipe Loureiro
Keywords: Modified Dirac operator
Axially symmetric functions
Hypermonogenic functions
Several vector variables.
Issue Date: Feb-2018
Publisher: Springer
Abstract: In this paper we introduce the modified Dirac operators $\mathcal{M}_{\m{x}}^\kappa f:= \,\partial_{\m{x}}f-\frac{\kappa}{x_m}e_m\cdot f$ and $\mathcal{M}_{\m{y}}^\tau f:= \,\partial_{\m{y}}f-\frac{\tau}{y_m}e_m \cdot f$, where $f:\Omega\subset \mathbb{R}_+^{m}\times \mathbb{R}_+^{m}\to\Cl_{0,m}$ is differentiable function, and $\Cl_{0,m}$ is the Clifford algebra generated by the basis vectors of $\mathbb{R}^m$. We look for solutions $f(\m{x},\m{y}) =f(\U{x},x_m,\U{y},y_m)$ of the system $\mathcal{M}_{\m{x}}^\kappa f(\m{x,y})= \mathcal{M}_{\m{y}}^\tau f(\m{x,y})=0$, where the first and third variables are invariant under rotations. These functions are called $(\kappa,\tau)$-hypermonogenic functions. We discuss about axially symmetric functions with respect to the symmetric group $SO(m-1)$. Some examples of axially symmetric $(\kappa,\tau)$-hypermonogenic functions generated by homogeneous functions and hypergeometric functions are presented.
Peer review: yes
URI: http://hdl.handle.net/10773/22094
DOI: 10.1007/s11785-017-0728-7
ISSN: 1661-8254
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