A mi-chemin entre analyse complexe et superanalyse
Complex Variables
2012-01-05 v2 Mathematical Physics
Classical Analysis and ODEs
math.MP
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.
Cite
@article{arxiv.1007.0819,
title = {A mi-chemin entre analyse complexe et superanalyse},
author = {Pierre Bonneau and Anne Cumenge},
journal= {arXiv preprint arXiv:1007.0819},
year = {2012}
}
Comments
version 2 : \`a para\^itre dans Publicacions Matem\`atiques (compl\'ements par rapport \`a la version 1 : commentaires sur les conditions alg\'ebriques)