On the uniform convergence of continuous semigroups

Manuel D. Contreras, Carlos Gómez-Cabello, Luis Rodríguez-Piazza

Let $\hat{I}\text{c◯}$ be a region in the complex plane $\mathbb{C}$ and let $\{\hat{I}{¦}_t{\}}_{t\ge 0}$ be a continuous semigroup of functions on $\hat{I}\text{c◯}$; that is, $\hat{I}{¦}_t:\hat{I}\text{c◯}\to \hat{I}\text{c◯}$ is holomorphic for every…