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

Classical Analysis and ODEs 2007-05-23 v1 Complex Variables

Authors: Vincent Thilliez

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Abstract

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.

Keywords

function theory special functions function spaces and inequalities

Cite

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

Comments

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

Abstract

Keywords

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