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Applications of Laplace–Carleson embeddings to admissibility and controllability

Jacob, Birgit; Partington, Jonathan R. and Pott, Sandra LU (2014) In SIAM Journal of Control and Optimization 52(2). p.1299-1313
Abstract
It is shown how results on Carleson embeddings induced by the Laplace transform can be used to derive new and more general results concerning the weighted (infinite-time) admissibility of control and observation operators for linear semigroup systems with q-Riesz bases of eigenvectors. As an example, the heat equation is considered. Next, a new Carleson embedding result is proved, which gives further results on weighted admissibility for analytic semigroups. Finally, controllability by smoother inputs is characterized by means of a new result about weighted interpolation.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
semigroup system, controllability, admissibility, Hardy space, weighted, Bergman space, interpolation, Carleson measure
in
SIAM Journal of Control and Optimization
volume
52
issue
2
pages
1299 - 1313
publisher
SIAM Publications
external identifiers
  • wos:000335820200021
  • scopus:84902686862
ISSN
1095-7138
DOI
10.1137/120894750
language
English
LU publication?
yes
id
b52b5954-2cc3-44b7-b95d-320dc1e1b3c9 (old id 4470467)
date added to LUP
2014-06-19 12:28:19
date last changed
2017-07-09 03:00:37
@article{b52b5954-2cc3-44b7-b95d-320dc1e1b3c9,
  abstract     = {It is shown how results on Carleson embeddings induced by the Laplace transform can be used to derive new and more general results concerning the weighted (infinite-time) admissibility of control and observation operators for linear semigroup systems with q-Riesz bases of eigenvectors. As an example, the heat equation is considered. Next, a new Carleson embedding result is proved, which gives further results on weighted admissibility for analytic semigroups. Finally, controllability by smoother inputs is characterized by means of a new result about weighted interpolation.},
  author       = {Jacob, Birgit and Partington, Jonathan R. and Pott, Sandra},
  issn         = {1095-7138},
  keyword      = {semigroup system,controllability,admissibility,Hardy space,weighted,Bergman space,interpolation,Carleson measure},
  language     = {eng},
  number       = {2},
  pages        = {1299--1313},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal of Control and Optimization},
  title        = {Applications of Laplace–Carleson embeddings to admissibility and controllability},
  url          = {http://dx.doi.org/10.1137/120894750},
  volume       = {52},
  year         = {2014},
}