arXiv subjects

Abdelhafed Elkhadiri

Publications and source records attributed to Abdelhafed Elkhadiri.

4 recordsLinked to original sources

arXiv2025

On some quasianalytic classes of $C^\infty$ functions

This expository article is devoted to the notion of quasianalytic classes and the Borel mapping. Although quasianalytic classes are well known in analysis since several decades. We are interested in certain properties of Denjoy-Carleman's quasianalytic classes, such as the non-surjectivity of the Borel mapping, the property of monotonicity. We try to see if it remains true for other quasianalytic classes, such as for example, the classes of indefinitely differentiable functions definable in a polynomially bounded o-minimal structures. What motivated this is the fact of having shown in a previous article the existence of quasianalytic classes where Borel mapping is surjective.

math.CA↗

arXiv2019

On some quasi-analytic classes

Using the so called monotonicity property, we prove that the Borel mapping restricted to some quasi-anlytic classes is never onto.

math.FA↗

arXiv2017

Some non noetherian $C^\infty$ quasianalytic local rings

We give an example of a non-noetherian quasi-analytic ring constructed using a quasi-analytic Denjoy-Carleman class. If we denote by $ \mathcal{D}_n$ the ring of those $ C^\infty$ quasianalytic function germs at $0\in \mathbb{R}^n$ which are definable in a polynomially bounded o-minimal structure. We show that the system $\{ \mathcal{D}_n\,/\, n\in\mathbb{N}^*\}$ is not noetherian, i.e. there exists $m\in\mathbb{N}$, $m > 1$, such that the ring $\mathcal{D}_m$ is not noetherian.

math.AG↗

arXiv2012

On connected components of some globally semi-analytic sets

We isolate a class, say $\mathcal{A}$, of global real analytic functions such that, each global semi-analytic set defined by $\mathcal{A}$ has only finitely many connected components and each component is also a global semi-analytic set defined by $\mathcal{A}$.

math.AG↗