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 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, a continuation theorem of Hartogs-Bochner type and a Liouville theorem for the superdifferentiable functions.

version 2 : à paraître dans Publicacions Matemàtiques (compléments par rapport à la version 1 : commentaires sur les conditions algébriques)