English

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

Complex Variables 2007-05-23 v1

Abstract

Given NN a non generic smooth CR submanifold of \CL\C^L, N={(\n,h(\n))}N=\{(\n,h(\n))\} where \n\n is generic in \CLn\C^{L-n} and hh is a CR map from \n\n into \Cn\C^n. We prove, using only elementary tools, that if hh is decomposable at p\np'\in \n then any decomposable CR distribution on NN at p=(p,h(p))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 NN is a smooth totally real submanifold of \CL\C^L any continuous function on NN admits a holomorphic extension to a complex transverse wedge

Keywords

Cite

@article{arxiv.math/0510184,
  title  = {Holomorphic extension of decomposable distributions from a CR submanifold of $\mathbb C^L$},
  author = {Nicolas Eisen},
  journal= {arXiv preprint arXiv:math/0510184},
  year   = {2007}
}

Comments

To appear in Michigan Math. Journal