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Operators, Functions, and Systems: An Easy Reading: Volume 2: Model Operators and Systems
Nikolai K. Nikolski, University of Bordeaux I, Talence, France
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Mathematical Surveys and Monographs
2002; 439 pp; softcover
Volume: 93
ISBN-10: 0-8218-5265-5
ISBN-13: 978-0-8218-5265-1
List Price: US$108 Member Price: US$86.40
Order Code: SURV/93.S

Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, Vol. 92, 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. Infinite-dimensional system theory and signal processing.

This volume contains Parts C and D.

Function models for linear operators and free interpolations: This is a universal topic and, indeed, is the most influential operator theory technique in the post-spectral-theorem era. In this book, its capacity is tested by solving generalized Carleson-type interpolation problems.

Infinite-dimensional system theory and signal processing: This topic is the touchstone of the three previously developed techniques. The presence of this applied topic in a pure mathematics environment reflects important changes in the mathematical landscape of the last 20 years, in that the role of the main consumer and customer of harmonic, complex, and operator analysis has more and more passed from differential equations, scattering theory, and probability to control theory and signal processing.

This and the companion volume are geared toward a wide audience of readers, from graduate students to professional mathematicians. They develop an elementary approach to the subject while retaining an expert level that can be applied in advanced analysis and selected applications.

Graduate students and research mathematicians interested in operator theory, functions of a complex variable, systems theory, and control.

Model operators and free interpolation
• Contents
• Foreword to part C
• The basic function model
• Elements of spectral theory in the language of the characteristic function
• Decompositions into invariant subspaces and free interpolation
Analytic problems in linear system theory
• Contents
• Foreword to part D
• Basic theory
• First optimizations: Multiplicity of the spectrum and the DISC
• Eigenvector decompositions, vector valued exponentials, and squared optimization
• A glance at bases of exponentials and of reproducing kernels
• A brief introduction to $$H^{\infty}$$ control
• Bibliography
• Author index
• Subject index
• Symbol index
• Errata to volume 1