4 papers
math.CA2006
Division by Flat Ultradifferentiable Functions and Sectorial Extensions
Vincent Thilliez
We consider classes of functions holomorphic in an open plane sector and belonging to a strongly non-quasianalytic class on the closure of . In $ \m…
math.CA2006
On the Stability of Analytic Germs under Ultradifferentiable Perturbations
Vincent Thilliez
Let be a real-analytic function germ whose critical locus contains a given real-analytic set , and let be a germ of closed subset of at the origin.…
math.CA2005
On quasianalytic local rings
Vincent Thilliez
This expository article is devoted to the local theory of ultradifferentiable classes of functions, with a special emphasis on the quasianalytic case. Although quasianalytic classe…
math.CA2004
Infinite determinacy on a closed set for smooth germs with non-isolated singularities
Vincent Thilliez
We give necessary and sufficient conditions of infinite determinacy for smooth function germs whose critical locus contains a given set. This set is assumed to be the zero variety…