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Book DetailsFields Institute MonographsVolume: 3; 1996; 339 ppMSC: Primary 47; Secondary 15; 34; 65; 93
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 copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipResearch mathematicians.

Table of Contents

Chapters

Lecture 1. Infinite matrices and projection methods

Lecture 2. Operator theory and ordinary differential operators

Lecture 3. Operators on indefinite inner product spaces

Lecture 4. State space theory of rational matrix functions and applications


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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 copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Research mathematicians.

Chapters

Lecture 1. Infinite matrices and projection methods

Lecture 2. Operator theory and ordinary differential operators

Lecture 3. Operators on indefinite inner product spaces

Lecture 4. State space theory of rational matrix functions and applications