Fields Institute Monographs 1996; 339 pp; hardcover Volume: 3 ISBN10: 082180457X ISBN13: 9780821804575 List Price: US$120 Member Price: US$96 Order Code: FIM/3
 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). Readership Research mathematicians. Table of Contents  Lecture Series 1. A. Böttcher, Infinite matrices and projection methods
 Matrix representation of operators
 Three problems for infinite matrices
 The finite section method
 Selfadjoint and compact opeators
 Toeplitz matrices with continuous symbols
 Toeplitz operators: algebraization of stability
 Toeplitz operators: localization
 Block case and higher dimensions
 Banach space phenomena
 Norms of inverses and pseudospectra
 Toeplitz determinants
 More general projection methods
 Bibliography
 Lecture Series 2. A. Dijksma and H. Langer, Operator theory and ordinary differential operators
 Introduction
 Definitizable operators in Kreĭn spaces
 Boundary eigenvalue problems for SturmLiouville operators and related holomorphic functions
 Operator representations of holomorphic functions
 SturmLiouville operators with indefinite weight
 Interface conditions and singular potentials
 Operator pencils
 Bibliography
 Symbols used in the lecture
 Lecture Series 3. M. A. Dritschel and J. Rovnyak, Operators on indefinite inner product spaces
 Introduction: Preliminaries and notation
 Kreĭn spaces and operators
 Julia operators and contractions
 Extension and completion problems
 The Schur algorithm
 Reproducing kernel Pontryagin spaces and colligations
 Invariant subspaces
 Bibliography
 Lecture Series 4. M. A. Kaashoek, State space theory of rational matrix functions and applications
 Introduction
 Canonical factorization and the state space method
 \(J\)unitary rational matrix functions
 Analysis of zeros
 Inverse problems involving null pairs
 Analysis of zeros and poles
 Inverse problems involving nullpole triples
 Bibliography
 Index
