# Diffusive systems and weighted Hankel operators

## TL;DR

This paper studies diffusive systems characterized by kernels as Fourier-Borel transforms and explores conditions under which associated weighted Hankel operators are bounded, Hilbert-Schmidt, or nuclear, extending previous mathematical results.

## Contribution

It generalizes existing results by establishing new conditions for the boundedness and nuclearity of weighted Hankel operators linked to diffusive systems.

## Key findings

- Conditions for boundedness of weighted Hankel operators
- Criteria for Hilbert-Schmidt and nuclear operators
- Extension of classical results to broader classes of diffusive systems

## Abstract

We consider diffusive systems, regarded as input/output systems with a kernel given as the Fourier--Borel transform of a measure in the left half-plane. Associated with these are a family of weighted Hankel integral operators, and we provide conditions for them to be bounded, Hilbert--Schmidt or nuclear, thereby generalizing results of Widom, Howland and others.