## 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…