I begun to write the book "Well-posed Linear Systems" on December 30,
1997. The main motivation for my desicion to write this book was that
the research papers that I had been writing grew longer and longer, as
each paper contained more and more overhead where I explained the
basic results that the reader was supposed to know before he/she could
absorb the results of the new paper.
In this book, there are very few results that I have borrowed directly
from some research papers (apart from what I have borrowed from
myself). Instead I have tried to read and absorb different results,
and then I have rewritten the proofs in a style that fits the rest of
the book. As a result, many of the proofs are now shorter that the
original ones in the sense that some part of the proof have been
transferred into the "basic theory", to which I can cite many times
from different places. I have tried to keep the book reasonably
self-contained. However, I have not included all the "exotic"
examples that you find in the literature; instead I give references to
these. Quite a few of the results are actually (at least formally)
new. See the introduction and the comments at the end of each chapter
for more details.
Already at the very beginning I expected this to be a long project
(like the writing of the book "Volterra Integral and Functional
Equations" was). As far as I can remember, I had the first drafts of
Chapters 2-5 ready in the summer of 1998. I made a huge progress
during the next academic year 1998-1999, while I had a research grant
from the Academy of Finland, which released me from all teaching and
administrative duties. After that the progress has been slower in the
sense that the number of pages no longer grew at a very rapid page;
instead the content kept changing. In the summer of 2000 the length of
the manuscript was approximately 500 pages, in the summer of 2002 it
was 720. The final length of the published book is 794 pages. The
publicatication date is March 1, 2005. The publisher is Cambridge
University Press, and it appears as number 103 in the series
"Encyclopedia of Mathematics and its Applications". An electronic
version will also be available from Cambridge shortly.
From the very beginning I kept a copy of the manuscript on my web page
(http://www.abo.fi/~staffans), hoping to get some feedback from the
readers. It did get some. At the beginning the versions that I kept
on my web page were changing at a rather rapid pace. I then slowed
down the turnaround, and posted two versions per year (one in January,
the other in July). For the last few years I have been citing the book
in my papers, sayings something like "for more details, see my book,
Sections so and so". So has many others. Because of this, there
already exists a number of citations to this book in the literature.
Since the book has now appeared I have removed these early versions
from my web page.
I wish you all a happy reading!