This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. The emphasis is on well-posedness, observability and controllability properties. The abstract results are supported by a large number of examples coming mostly from partial differential equations. These examples are worked out in detail. This book is meant to be an elementary introduction in this theory. The first meaning of "elementary'' is that the text is aimed to be accessible to any reader familiar with linear algebra, calculus, the basics of Hilbert spaces and differential equations. We introduce everything needed on operator semigroups and most of the background used is summarized in the Appendices, often with proofs. The second meaning of "elementary'' is that we only cover results for which we can provide complete proofs. In our bibliographic comments we mention some of the more advanced results, for example those based on microlocal analysis.

*Observation and control for operator semigroups.* Edited by: Amann, H; Krantz, S G; Kumar, S; Nekovar, J (2009). Basel: Birkhäuser.

## Abstract

This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. The emphasis is on well-posedness, observability and controllability properties. The abstract results are supported by a large number of examples coming mostly from partial differential equations. These examples are worked out in detail. This book is meant to be an elementary introduction in this theory. The first meaning of "elementary'' is that the text is aimed to be accessible to any reader familiar with linear algebra, calculus, the basics of Hilbert spaces and differential equations. We introduce everything needed on operator semigroups and most of the background used is summarized in the Appendices, often with proofs. The second meaning of "elementary'' is that we only cover results for which we can provide complete proofs. In our bibliographic comments we mention some of the more advanced results, for example those based on microlocal analysis.

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## Additional indexing

Item Type: | Edited Scientific Work |
---|---|

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2009 |

Deposited On: | 08 Jun 2009 14:52 |

Last Modified: | 14 Sep 2016 13:39 |

Publisher: | Birkhäuser |

Series Name: | Birkhäuser Advanced Texts / Basler Lehrbücher |

Number of Pages: | 483 |

ISBN: | 978-3-7643-8993-2 |

Publisher DOI: | https://doi.org/10.1007/978-3-7643-8994-9 |

Official URL: | http://www.springer.com/birkhauser/mathematics/book/978-3-7643-8993-2 |

Related URLs: | http://www.recherche-portal.ch/primo_library/libweb/action/search.do?fn=search&mode=Advanced&vid=ZAD&vl%28186672378UI0%29=isbn&vl%281UI0%29=contains&vl%28freeText0%29=978-3-7643-8993-2 |

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