Tag: log-exp analytic

Ilyashenko algebras based on definable monomials, revisited

PatrickKonstanz working seminar / Quasianalytic asymptotic algebras / Research1 Comment

In order to address some of the questions raised in this post, I introduce here some relevant definitions and recast the construction of Ilyashenko algebras based on $\log$ monomials using these new notions. As before, let $\H$ be the Hardy field of germs at $+\infty$ of all $h:\RR \into \RR$ definable in $\Ranexp$, and denote…

The Hardy field of $\,\Ranexp$

PatrickKonstanz working seminar / Log-exp analytic functions / Research1 Comment

(Joint work with Tobias Kaiser) The goal of this post is to describe the Hardy field $\H = \Hanexp$ of the expansion $\Ranexp$ of the real field by all restricted analytic functions and the exponential function, based on van den Dries, Macintyre and Marker’s papers on $\Ranexp$ and on LE-series. In particular, the first paper…

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