Applications of Laplace-Carleson embeddings to admissibility and controllability

It is shown how results on Carleson embeddings induced by the Laplace transform can be use to derive new and more general results concerning the weighted admissibility of control and observation operators for linear semigroup systems with q-Riesz bases of eigenvectors. Next, a new Carleson embedding result is proved, which gives further results on weighted admissibility for analytic semigroups. Finally, controllability by smoother inputs is characterised by means of a new result about weighted interpolation.