Open Access
2012 A mi-chemin entre analyse complexe et superanalyse
Pierre Bonneau, Anne Cumenge
Publ. Mat. 56(1): 3-40 (2012).


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 $\mathbb{C}$). Under the condition $(A)$, we get an integral representation formula for the superdifferentiable functions. We deduce properties of the superdifferentiable functions: analyticity, a result of separated superdifferentiability, a Liouville theorem and a continuation theorem of Hartogs-Bochner type.


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Pierre Bonneau. Anne Cumenge. "A mi-chemin entre analyse complexe et superanalyse." Publ. Mat. 56 (1) 3 - 40, 2012.


Published: 2012
First available in Project Euclid: 15 December 2011

zbMATH: 1284.30043
MathSciNet: MR2918182

Primary: 30E20 , 30G30 , 32A26 , 35C15

Keywords: integral representation , superanalysis , superdifferentiable function , Superspace

Rights: Copyright © 2012 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.56 • No. 1 • 2012
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