Vincent Thilliez

activity

20042019

most citedOn quasianalytic local rings

46 citations · 68 across the 6 of their papers we have counts for

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8 papers · 1 filter

math.CA2019

Functions with ultradifferentiable powers

Vincent Thilliez

We study the regularity of smooth functions $f$ defined on an open set of $R^{n}$ and such that, for certain integers $p \geq 2$ , the powers $f^{p} : x \mapsto (f (x))^{p}$ belong t…

math.CA2012

Łojasiewicz ideals in Denjoy-Carleman classes

Vincent Thilliez

The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a…

math.CA2010★ 3 cited

On the non-extendability of quasianalytic germs

Vincent Thilliez

Let $E_{1} (M)^{+}$ be the local ring of germs at 0 of functions belonging to a given Denjoy-Carleman quasianalytic class in a neighborhood of 0 in $[0, + \infty [$ . We show that…

math.CA2008★ 19 cited

Smooth solutions of quasianalytic or ultraholomorphic equations

Vincent Thilliez

In the first part of this work, we consider a polynomial $ϕ (x, y) = y^{d} + a_{1} (x) y^{d - 1} + ... + a_{d} (x)$ whose coefficients $a_{j}$ belong to a Denjoy-Carleman quasianalytic local ring $ \…

math.CA2006

Division by Flat Ultradifferentiable Functions and Sectorial Extensions

Vincent Thilliez

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 $ \m…

math.CA2006

On the Stability of Analytic Germs under Ultradifferentiable Perturbations

Vincent Thilliez

Let $f$ be a real-analytic function germ whose critical locus contains a given real-analytic set $X$ , and let $Y$ be a germ of closed subset of $R^{n}$ at the origin.…