On ultradifferentiable functions
Classical Analysis and ODEs
2017-02-14 v6
Abstract
We give complete and exact descriptions of spaces of ultradifferentiable functions that are closed under composition with either holomorphic or ultradifferentiable functions -- which are two distinct cases. The proof works by considering formal power series, and stability under differentiation is not required. As an application of the power series approach we reprove regularity results for solutions of ode's and pde's without employing tedious estimates imploying the Fa\`a di Bruno formula for higher derivatives of composite maps.
Cite
@article{arxiv.1605.07528,
title = {On ultradifferentiable functions},
author = {Jürgen Pöschel},
journal= {arXiv preprint arXiv:1605.07528},
year = {2017}
}
Comments
25 pages. Withdrawn and superseded by an extended version with the title "On the Siegel-Sternberg linearization theorem:"