3 research outputs found
Laplace--Carleson embeddings on model spaces and boundedness of truncated Hankel and Toeplitz operators
A characterisation is given of bounded embeddings from weighted spaces
on bounded intervals into spaces on the half-plane, induced by
isomorphisms given by the Laplace transform onto weighted Hardy and Bergman
spaces (Zen spaces). As an application necessary and sufficient conditions are
given for the boundedness of truncated Hankel and Toeplitz integral operators,
including the weighted case.Comment: 19 pages. Some minor revision
Admissibility of retarded diagonal systems with one-dimensional input space
We investigate infinite-time admissibility of a control operator in a
Hilbert space state-delayed dynamical system setting of the form
, where generates a diagonal
-semigroup, is also diagonal and . Our approach is based on the Laplace embedding
between and the Hardy space . The results are
expressed in terms of the eigenvalues of and and the sequence
representing the control operator.Comment: 25 pages, 2 figure