Before showing the Table of contents of this book, we would like briefly to explain our motivation to the subject. In the mid-eighties, J.-L. Lions contributed to the multiplier method by proving powerful and elegant theorems on observability, controllability, and uniform stabilization. His 1988 survey article and monograph also stimulated intensive research activity in the field.
The multiplier method led to great success, but several problems remained unsolved. Starting research on them, we came up with another efficient way to deal with those issues: using a former approach based on harmonic analysis.
Indeed, following the influential survey paper of D.L. Russell (1978), many authors had emphasized a classical result of A.E. Ingham (1936) for its
simplicity and depth that had proven to be extremely useful in control theory.
In this book, our purpose is to unify, as much as possible, the so-called
harmonic (or nonharmonic) analysis method. It is also to make the subject
as simple as possible. We start by solving elementary “ad hoc” controllability
problems; then we extend the results and the proofs to a general framework.
The book contains almost all proofs of the theorems, and only little knowledge
of functional analysis is required.Many results presented here are new and still
unpublished, while many known results have been rewritten for the purpose
of simplification.
The last part of this book is devoted to the exposition and the derivation
of some joint results with C. Baiocchi. We would like to take this opportunity
to thank him for his precious contribution to our work. We are also grateful
to all our students and colleagues for their encouragement as well as for their
interest through very useful discussions and comments. Finally, we wish to
thank the editorial staff at Springer-Verlag, New York, for their help and
support.
Rome and Strasbourg, August 2003
The multiplier method led to great success, but several problems remained unsolved. Starting research on them, we came up with another efficient way to deal with those issues: using a former approach based on harmonic analysis.
Indeed, following the influential survey paper of D.L. Russell (1978), many authors had emphasized a classical result of A.E. Ingham (1936) for its
simplicity and depth that had proven to be extremely useful in control theory.
In this book, our purpose is to unify, as much as possible, the so-called
harmonic (or nonharmonic) analysis method. It is also to make the subject
as simple as possible. We start by solving elementary “ad hoc” controllability
problems; then we extend the results and the proofs to a general framework.
The book contains almost all proofs of the theorems, and only little knowledge
of functional analysis is required.Many results presented here are new and still
unpublished, while many known results have been rewritten for the purpose
of simplification.
The last part of this book is devoted to the exposition and the derivation
of some joint results with C. Baiocchi. We would like to take this opportunity
to thank him for his precious contribution to our work. We are also grateful
to all our students and colleagues for their encouragement as well as for their
interest through very useful discussions and comments. Finally, we wish to
thank the editorial staff at Springer-Verlag, New York, for their help and
support.
Rome and Strasbourg, August 2003
0 on: "Fourier Series in Control Theory"
If some URL not work please inform me and thanks