18 citations · 69 across the 34 of their papers we have counts for
44 papers
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…
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…
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…
Relative differential closure in Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conj…
The theory of maximal Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that all maximal Hardy fields are elementarily equivalent as differential fields to the differential field of transseries, and give various applications of this…
The reciprocal complement of a polynomial ring in several variables over a field
Neil Epstein, Lorenzo Guerrieri, K. Alan Loper
The *reciprocal complement* of an integral domain is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of ar…