Abstract
In this paper, we establish the connection between supermonogenic functions (i.e. solutions to the Dirac equation in superspace) and -supermonogenic functions (i.e. solutions to the higher order Dirac equations in superspace) by an expansion of Almansi type for -supermonogenic functions. The expansion generalizes the classical Almansi expansion for polyharmonic functions as well as the Fischer decomposition of polynomials. In order to obtain the expansion, we construct the 0-normalized system of functions with respect to the Dirac operator in superspace. Moreover, using the system we get a non-trivial solution to the modified Dirac equation in superspace which is closely related to Helmholtz equation.
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