Division by Flat Ultradifferentiable Functions and Sectorial Extensions

@inproceedings{Thilliez2006DivisionBF,
  title={Division by Flat Ultradifferentiable Functions and Sectorial Extensions},
  author={Vincent Thilliez},
  year={2006}
}
  • Vincent Thilliez
  • Published 2006
We consider classes 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 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 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 ∞ result of… CONTINUE READING

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