A mi-chemin entre analyse complexe et superanalyse

TL;DR

This paper develops a superanalysis framework that extends complex analysis concepts to superalgebras, providing integral formulas, continuation theorems, and Liouville results for superdifferentiable functions.

Contribution

It introduces a generalized superanalysis theory under a specific algebraic condition, extending classical complex analysis results to superalgebras.

Findings

Derived an integral representation formula for superdifferentiable functions.

Established a Hartogs-type separated superdifferentiability result.

Proved a Liouville theorem for superdifferentiable functions.

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.