On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis (Q734080)

The first-order differential operator (called Dirac operator) \[ \partial_{\underline X}= \sum^n_{j=1} e_j\partial_{X_j} \] and the so-called twisted Dirac operator \[ \partial_{\underline X}= \sum^n_{j=1} (e_j\partial_{y_j}- e_{n+j}\partial_{x_j}) \] are simultaneously considered within the theory of Hermitean Clifford analysis. Hermitean monogenic functions are introduced as common null functions of the Dirac operator and the twisted Dirac operator. In this very general setting, Clifford-Stokes theorems and Hermitean Cauchy-Pompeiu formulae are proved. For spinor valued functions, a Martinelli-Bochner formula for holomorphic functions of several complex variables can be deduced from the Hermitean Cauchy integral formula.