Division by Flat Ultradifferentiable Functions and Sectorial Extensions

Vincent Thilliez

doi:10.1007/s00025-003-0081-1

Division by Flat Ultradifferentiable Functions and Sectorial Extensions

经典分析与常微分方程 2007-05-23 v1 复变函数

作者: Vincent Thilliez

在 arXiv 上查看 ↗ PDF ↗ DOI ↗

摘要

We consider classes $\mathcal{A}_M(S)$ of functions holomorphic in an open plane sector $S$ and belonging to a strongly non-quasianalytic class on the closure of $S$ . In $\mathcal{A}_M(S)$ , we construct functions which are flat at the vertex of $S$ with a sharp rate of vanishing. This allows us to obtain a Borel-Ritt type theorem for $\mathcal{A}_M(S)$ extending previous results by Schmets and Valdivia. We also derive a division property for ideals of flat ultradifferentiable functions, in the spirit of a classical $C^\infty$ result of Tougeron.

关键词

function theory special functions function spaces and inequalities

引用

@article{arxiv.math/0602366,
  title  = {Division by Flat Ultradifferentiable Functions and Sectorial Extensions},
  author = {Vincent Thilliez},
  journal= {arXiv preprint arXiv:math/0602366},
  year   = {2007}
}

备注

Slight update of the published version. The definition of closedness in subsections 4.1 and 4.2 is less restrictive. One minor typo corrected

Division by Flat Ultradifferentiable Functions and Sectorial Extensions

摘要

关键词

引用

备注

相关论文