Abstract: 

We introduce a notion of analytic generator for groups of unbounded 
operators, on Banach modules, arising
from Esterle's quasimultiplier theory. Characterizations of analytic 
generators are given in terms of the existence 
of certain functional calculi. This extends recent results about $C_0$ groups 
of bounded operators. The theory is
applicable to sectorial operators, representations of $H^\infty$, and 
integrated groups.

1. Departamento de Matemáticas
   Universidad de Zaragoza
   50009 Zaragoza
   Spain