Fischer decomposition and special solutions for the parabolic Dirac operator

In this paper we study a Fischer decomposition for the parabolic Dirac operator which factorizes the heat equation. Since the standard construction techniques are not valid in our case, due to the non-homogeneity of the positive parabolic Dirac operator, we first establish and study the Fischer decomposition for the homogeneous part of the parabolic Dirac operator. Finally, we construct nullsolutions of the parabolic Dirac operator by means of series expansions in terms of cylindrical co-ordinates.