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Stochastic processes and financial applicationsHolomorphic and Operator TheoryNonlinear Differential Equations Analysis

Constructing ω-free Hardy fields

M. Aschenbrenner, Lou van den Dries, J. van der Hoeven

2026.4.19JOURNAL D ANALYSE MATHEMATIQUE

DOI: 10.1007/s11854-026-0447-y

Abstract

Abstract We show that every Hardy field extends to an ω-free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations. It is essential in [10], and here we apply it to answer questions of Boshernitzan, and to generalize a theorem of his.

Citation format

ASCHENBRENNER, M.; DRIES, Lou van den; HOEVEN, J. van der. Constructing ω-free hardy fields. JOURNAL D ANALYSE MATHEMATIQUE, 2026.