Entre analyse complexe et superanalyse

Pierre Bonneau (1) , Anne Cumenge (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Superanalyse; super-differentiablité; représentation intégrale.

Mots clés: représentation intégrale

Domaines: Variables complexes [math.CV]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Pierre Bonneau, Anne Cumenge. Entre analyse complexe et superanalyse. 2009. ⟨hal-00424624v1⟩