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

Mots clés: superspace; superdifferentiable function; integral representation; superanalysis

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

Pierre Bonneau, Anne Cumenge. A mi-chemin entre analyse complexe et superanalyse. Publicacions Matemàtiques, 2012, 56 (1), pp.3-40. ⟨10.5565/PUBLMAT_56112_01⟩. ⟨hal-00497218v2⟩