2024/12/14 by Matthias Aschenbrenner, Lou van den Dries, Aschenbrenner, Matthias +3
Computer Science · Engineering · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2412.10764
openalex publication_date 2024/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 conjecture of Boshernitzan (1981): the intersection of all maximal analytic Hardy fields agrees with that of all maximal Hardy fields. We also generalize a key ingredient in the proof, and describe a cautionary example delineating the boundaries of its applicability.