Description 
1 online resource (xi, 483 pages) : illustrations 
Series 
Birkhäuser advanced texts 

Birkhäuser advanced texts.

Contents 
Preface  1. Finitedimensional Systems  2. Operator Semigroups  3. Semigroups of Contractions  4. Control and Observation Operators  5. Observability  6. Observation for the Wave Equation  7. Nonharmonic Fourier Series and Exact Observability  8. Observability for Parabolic Equations  9. Boundary Control Systems  10. Controllability  Appendices  References 
Summary 
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 wellposedness, 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 
Bibliography 
Includes bibliographical references (pages 459474) and index 
Notes 
Print version record 
Subject 
Linear operators.


Semigroups of operators.

Form 
Electronic book

Author 
Weiss, George, 1956

LC no. 
2008941510 
ISBN 
376438994X (eisbn) 

9783764389949 (eisbn) 
