Nonlinear Conditions for Ultradifferentiability
David Nicolas Nenning1, Armin Rainer1, Gerhard Schindl1
1Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria.
Abstract:
A remarkable theorem of Joris states that a function f is if two relatively prime powers of f are . Recently, Thilliez showed that an analogous theorem holds in Denjoy-Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris's result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.
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