Entre analyse complexe et superanalyse
Pierre Bonneau (IMT), Anne Cumenge (IMT)
TL;DR
This paper develops a superanalysis framework that parallels complex analysis, providing integral representation formulas and extension theorems for superdifferentiable functions under specific algebraic conditions.
Contribution
It introduces a superanalysis theory with integral formulas and Hartogs-type theorems, extending complex analysis concepts to superalgebras under condition (A).
Findings
Integral representation formula for superdifferentiable functions.
Hartogs-type separated superdifferentiability result.
Hartogs-Bochner continuation 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. 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.