A mi-chemin entre analyse complexe et superanalyse

Details A mi-chemin entre analyse complexe et superanalyse A mi-chemin entre analyse complexe et superanalyse

2010-07-06

arxiv.org/abs/1007.0819v2

Publicacions Matem\`atiques 56, 1 (2012) 3-40

Mathematics

Complex Variables

version 2 : \`a para\^itre dans Publicacions Matem\`atiques (compl\'ements par rapport \`a la version 1 : commentaires sur les

Scientific paper

10.5565/PUBLMAT_56112_01

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.

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