In preparing the second edition, I have taken advantage of the
opportunity to correct errors as well as revise the presentation in
many places. New material has been included, in addition,
reflecting relevant recent work. The help of many colleagues (and
especially Professor J. Stoer) in ferreting out errors is
gratefully acknowledged. I also owe special thanks to Professor v.
Sazonov for many discussions on the white noise theory in Chapter
6. February, 1981 A. V. BALAKRISHNAN v Preface to the First Edition
The title "Applied Functional Analysis" is intended to be short for
"Functional analysis in a Hilbert space and certain of its
applications," the applications being drawn mostly from areas
variously referred to as system optimization or control systems or
systems analysis. One of the signs of the times is a discernible
tilt toward application in mathematics and conversely a greater
level of mathematical sophistication in the application areas such
as economics or system science, both spurred undoubtedly by the
heightening pace of digital computer usage. This book is an entry
into this twilight zone. The aspects of functional analysis treated
here are rapidly becoming essential in the training at the advance
graduate level of system scientists and/or mathematical economists.
There are of course now available many excellent treatises on
functional analysis.
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