2015/03/23 by J.-P. Rolin, T. Servi · 1 citation
Mathematics · Computer Science · #Mathematical and Theoretical Analysis #Advanced Algebra and Logic #Advanced Topics in Algebra
paper · doi:10.1112/plms/pdv010
We consider for every n ∈ N an algebra A n of germs at 0 ∈ R n of continuous real-valued functions, such that we can associate to every germ f ∈ A n a (divergent) series T ( f ) with non-negative real exponents, which can be thought of as an asymptotic expansion of f. We require that the R-algebra homomorphism f ↦ 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.