Weighted multiple interpolation and the control of perturbed semigroup systems

TL;DR

This paper investigates the controllability and admissibility of perturbed semigroup systems using interpolation and Carleson measures, introducing new results on measure perturbations and weighted interpolation in Hardy spaces.

Contribution

It presents novel results on perturbation of Carleson measures and weighted interpolation, advancing the understanding of control in perturbed semigroup systems.

Findings

New criteria for controllability and admissibility of perturbed systems

Results on perturbation of Carleson measures

Advances in weighted interpolation in Hardy spaces

Abstract

In this paper the controllabillity and admissibility of perturbed semigroup systems are studied, using tools from the theory of interpolation and Carleson measures. In addition, there are new results on the perturbation of Carleson measures and on the weighted interpolation of functions and their derivatives in Hardy spaces, which are of interest in their own right.