**Fields Institute Monographs**

Volume: 3;
1996;
339 pp;
Hardcover

MSC: Primary 47;
Secondary 15; 34; 65; 93

Print ISBN: 978-0-8218-0457-5

Product Code: FIM/3

List Price: $126.00

Individual Member Price: $100.80

**Electronic ISBN: 978-1-4704-3130-3
Product Code: FIM/3.E**

List Price: $126.00

Individual Member Price: $100.80

# Lectures on Operator Theory and Its Applications

Share this page *Editors and Authors: *
*Peter Lancaster; Albrecht Böttcher; Aad Dijksma; Heinz Langer; Michael A. Dritschel; James Rovnyak; Marinus A. Kaashoek*

A co-publication of the AMS and Fields Institute

Much of the importance of mathematics lies in its ability
to provide theories which are useful in widely different fields
of endeavor. A good example is the large and amorphous body of
knowledge known as “the theory of linear operators”
or “operator theory”, which came to life about a century
ago as a theory to encompass properties common to matrix,
differential, and integral operators. Thus, it is a primary purpose of
operator theory to provide a coherent body of knowledge which can
explain phenomena common to the enormous variety of problems in which
such linear operators play a part. The theory is a vital part
of “functional analysis”, whose methods and techniques
are one of the major advances of twentieth century mathematics and
now play a pervasive role in the modeling of phenomena in
probability, imaging, signal processing, systems theory, etc., as well
as in the more traditional areas of theoretical physics and
mechanics.

This book is based on lectures presented at a meeting on
operator theory and its applications held at the Fields Institute in the
fall of 1994. The purpose of the meeting was to provide
introductory lectures on some of the methods being used and problems
being tackled in current research involving operator theory.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## Lectures on Operator Theory and Its Applications

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- Lecture 1. Infinite matrices and projection methods 114
- Lecture 2. Operator theory and ordinary differential operators 7386
- Lecture 3. Operator on indefinite inner product spaces 141154
- Lecture 4. State space theory of rational matrix functions and applications 233246
- Index 335348
- Back Cover Back Cover1354

#### Readership

Research mathematicians.