Publication Date:
2015-05-05
Description:
We consider for every $n\in \mathbb {N}$ an algebra $\mathcal {A}_{n}$ of germs at $0\in \mathbb {R}^{n}$ of continuous real-valued functions, such that we can associate to every germ $f\in \mathcal {A}_{n}$ a (divergent) series $\mathcal {T}(f)$ with non-negative real exponents, which can be thought of as an asymptotic expansion of $f$ . We require that the $\mathbb {R}$ -algebra homomorphism $f\mapsto \mathcal {T}(f)$ be injective (quasianalyticity property). In this setting, we prove analogue results to Denef and van den Dries’ quantifier elimination theorem and Hironaka's rectilinearization theorem for subanalytic sets.
Print ISSN:
0024-6115
Electronic ISSN:
1460-244X
Topics:
Mathematics