Analytic Hardy fields

Abstract

We show that maximal analytic Hardy fields are $\hat{I}{\cdot }_1$ in the sense of Hausdorff. We also prove various embedding theorems about analytic Hardy fields. For example, the ordered differential field $\mathbb{T}$ of transseries is shown to be isomorphic to an analytic Hardy field.

42 pp.; to appear in Compos. Math