Balakrishnan A.V. Applied Functional Analysis

Springer-Verlag, 1981. - 373 pages.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.
However, the very fact of the comprehensive coverage makes it difficult of access to the application-minded user, Also, the high degree of generality, the watermark of mathematical achievement. is often at the expense of the richer results obtainable in the more highly structured cases common in applications. It is with some of these thoughts in mind that I have dealt exclusively with analysis in a Hilbert space and emphasized such special topics as Volterra operators and Hilbert-Schmidt operators; dissipative compact semigroups; and factorization theorems for positive definite operators, to name a few, Many topics in functional analysis per se have had to be totally shelved or otherwise abridged considerably mostly based on considerations of significance in application, but also to keep the size of the volume within reasonable bounds.