Abstract
The following paper deals with the characterization of the polynomial null solutions for a homogeneous and a non-homogeneous parabolic Dirac operator, via Cauchy-Riemann-like systems. For that we will use the factorizations of the Laplace and the heat operator, respectively. We will present a Fischer decomposition for the case of homogeneous polynomials. At the end of the paper two examples are presented.
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