Mathematical Surveys and Monographs 2002; 461 pp; softcover Volume: 92 ISBN10: 0821849336 ISBN13: 9780821849330 List Price: US$113 Member Price: US$90.40 Order Code: SURV/92.S
 Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 2: Model Operators and Systems, Mathematical Surveys and Monographs, Vol. 93, AMS, 2002, this unique work combines four major topics of modern analysis and its applications: A. Hardy classes of holomorphic functions, B. Spectral theory of Hankel and Toeplitz operators, C. Function models for linear operators and free interpolations, and D. Infinitedimensional system theory and signal processing. This volume contains Parts A and B. Hardy classes of holomorphic functions is known to be the most powerful tool in complex analysis for a variety of applications, starting with Fourier series, through the Riemann \(\zeta\)function, all the way to Wiener's theory of signal processing. Spectral theory of Hankel and Toeplitz operators becomes the supporting pillar for a large part of harmonic and complex analysis and for many of their applications. In this book, moment problems, NevanlinnaPick and Carathéodory interpolation, and the best rational approximations are considered to illustrate the power of Hankel and Toeplitz operators. The book is geared toward a wide audience of readers, from graduate students to professional mathematicians, interested in operator theory and functions of a complex variable. The two volumes develop an elementary approach while retaining an expert level that can be applied in advanced analysis and selected applications. Readership Graduate students and research mathematicians interested in analysis. Table of Contents An invitation to Hardy classes/Contents  Foreword to Part A
 Invariant subspaces of \(L^2(\mu)\)
 First applications
 \(H^p\) classes. Canonical factorization
 Szegö infimum, and generalized PhragménLindelöf principle
 Harmonic analysis in \(L^2(\mathbb{T},\mu)\)
 Transfer to the halfplane
 Timeinvariant filtering
 Distance formulae and zeros of the Riemann \(\zeta\)function
Hankel and Toeplitz operators/Contents  Foreword to Part B
 Hankel operators and their symbols
 Compact Hankel operators
 Applications to NevanlinnaPick interpolation
 Essential spectrum. The first step: Elements of Toeplitz operators
 Essential spectrum. The second step: The Hilbert matrix and other Hankel operators
 Hankel and Toeplitz operators associated with moment problems
 Singular numbers of Hankel operators
 Trace class Hankel operators
 Inverse spectral problems, stochastic processes and onesided invertibility
 Bibliography
 Author index
 Subject index
 Symbol index
