10 papers
Normalizing Asymptotic Differential Equations
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection wit…
Constructing -free Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that every Hardy field extends to an -free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations…
Revisiting second-order linear differential equations over Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We review second-order homogeneous linear differential equations with coefficient functions whose germs lie in a Hardy field (and hence are strongly non-oscillating). We prove a co…
Analytic Hardy fields
Matthias Aschenbrenner, Lou van den Dries
We show that maximal analytic Hardy fields are in the sense of Hausdorff. We also prove various embedding theorems about analytic Hardy fields. For example, the ordered diff…
Whitney Approximation: domains and bounds
Matthias Aschenbrenner
We investigate properties of holomorphic extensions in the one-variable case of Whitney's Approximation Theorem on intervals. Improving a result of Gauthier-Kienzle, we construct t…
Short Hardy fields
Matthias Aschenbrenner, Lou van den Dries
Differentially algebraic Hardy field extensions of short Hardy fields are short. This is proved in the more general setting of -fields. As an application we extend a theorem of…