A mi-chemin entre analyse complexe et superanalyse

Abstract

In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition $(A)$ on the real superalgebras in consideration (this condition is a generalization of the classical relation $1 + i^2 = 0$ in $\mathbb{C}$). Under the condition $(A)$, we get an integral representation formula for the superdifferentiable functions. We deduce properties of the superdifferentiable functions: analyticity, a result of separated superdifferentiability, a Liouville theorem and a continuation theorem of Hartogs-Bochner type.