Laplace-Carleson embeddings and weighted infinite-time admissibility

TL;DR

This paper characterizes when Laplace-Carleson embeddings are bounded and applies these results to determine weighted infinite-time admissibility of control and observation operators.

Contribution

It provides necessary and sufficient conditions for bounded Laplace-Carleson embeddings and links these to weighted infinite-time admissibility in control theory.

Findings

Established criteria for bounded Laplace-Carleson embeddings.

Characterized weighted infinite-time admissibility of control and observation operators.

Connected embedding properties with control theory concepts.

Abstract

In this paper we will establish necessary and sufficient conditions for a Laplace-Carleson embedding to be bounded for certain spaces of functions on the positive half-line. We will use these results to characterise weighted (infinite-time) admissibility of control and observation operators.