arXiv subjects

Nicolas Eisen

Publications and source records attributed to Nicolas Eisen.

2 recordsLinked to original sources

arXiv2005

Holomorphic extension of decomposable distributions from a CR submanifold of $\mathbb C^L$

Given $N$ a non generic smooth CR submanifold of $\C^L$, $N=\{(\n,h(\n))\}$ where $\n$ is generic in $\C^{L-n}$ and $h$ is a CR map from $\n$ into $\C^n$. We prove, using only elementary tools, that if $h$ is decomposable at $p'\in \n$ then any decomposable CR distribution on $N$ at $p=(p',h(p'))$ extends holomorphically to a complex transversal wedge. This gives an elementary proof of the well known equivalent for totally real non generic submanifolds, i.e if $N$ is a smooth totally real submanifold of $\C^L$ any continuous function on $N$ admits a holomorphic extension to a complex transverse wedge

math.CV↗

arXiv2005

On the Holomorphic Extension of CR Distributions from Non Generic CR Submanifolds of $\C^L$

We give a holomorphic extension result from non generic CR submanifold of $\C^L$ of positive CR dimension. We consider $N$ a non generic CR submanifold given by $N=\{\n,h(\n)\}$ where $\n$ is a generic submanifold of some $\C^{\ell}$ and $h$ is a CR map from $\n$ into $\C^n$. We prove that if $\n$ is a hypersurface then any CR distribution on $N$ extends holomorphically to a complex transversal wedge, we then generalize this result for arbitrary $\n$ in the case where the graphing function $h$ is decomposable at some $p'\in \n$. We show that any CR distribution on $N$ that is decomposable at $p=(p',h(p'))$ extends holomorphically to a complex transversal wedge.

math.CV↗