A Phragmén-Lindelöf theorem via proximate orders, and the propagation of asymptotics

Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl

We prove that, for asymptotically bounded holomorphic functions in a sector in $\mathbb{C}$, an asymptotic expansion in a single direction towards the vertex with constraints in te…