Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator

Abstract

In the present article we study basic aspects of the symplectic version of Clifford analysis associated to the symplectic Dirac operator. Focusing mostly on the symplectic vector space of real dimension $2$, this involves the analysis of first order symmetry operators, symplectic Clifford-Fourier transform, reproducing kernel for the symplectic Fischer product and the construction of bases of symplectic monogenics for the symplectic Dirac operator.