## Analytic continuation of $\log$-$\exp$-analytic germs

Our preprint on the analytic continuation of germs at $+\infty$ of unary functions definable in $\Ranexp$ is now on the ArXiv. Here is its introduction: The o-minimal structure $\Ranexp$, see van den Dries and Miller or van den Dries, Macintyre and Marker, is one of the most important regarding applications, because it defines all elementary…

## Holomorphic extensions of definable germs

(Joint work with Tobias Kaiser) Recall from this post that not all germs in $\H$ have a holomorphic extension that maps definable real domains to definable real domains. In fact, the extension $\t_a$ of the translation $t_a$, for $a\gt 0$, does not even map real domains to real domains. So, in order to describe the…

## Some holomorphic extensions

(Joint work with Tobias Kaiser) We are interested in holomorphic extensions of one-variable functions definable in $\Ranexp$. Since $\exp$ and $\log$ are two crucial functions definable in $\Ranexp$, the natural domain on which to consider holomorphic extensions of all definable functions is the Riemann surface of the logarithm $$\LL:= (0,\infty) \times \RR$$ with its usual…

## The Hardy field of $\,\Ranexp$

(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…