A MI-CHEMIN ENTRE ANALYSE COMPLEXE ET SUPERANALYSE

作者：Bonneau Pierre^*; Cumenge Anne

来源：Publicacions Matematiques, 2012, 56(1): 3-40.

DOI：10.5565/PUBLMAT_56112_01

• superspace
• superdifferentiable function
• integral representation
• super-analysis

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 deduce properties of the superdifferentiable functions: analyticity, a result of separated superdifferentiability, a Liouville theorem and a continuation theorem of Hartogs-Bochner type.

• 出版日期2012