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 C ). Under the condition (A), we get an integral representation formula for the superdifferentiable functions. We give a result of Hartogs type of separated superdifferentiability and a continuation theorem of Hartogs–Bochner type for the superdifferentiable functions. To cite this article: P. Bonneau, A. Cumenge, C. R. Acad. Sci. Paris, Ser. I 347 (2009).