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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
Available Formats:
Softcover ISBN: 978-0-8218-5265-1
Product Code: SURV/93.S
List Price: $108.00 MAA Member Price:$97.20
AMS Member Price: $86.40 Electronic ISBN: 978-1-4704-1320-0 Product Code: SURV/93.S.E List Price:$108.00
MAA Member Price: $97.20 AMS Member Price:$86.40
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List Price: $162.00 MAA Member Price:$145.80
AMS Member Price: $129.60 Click above image for expanded view Operators, Functions, and Systems: An Easy Reading: Volume 2: Model Operators and Systems Nikolai K. Nikolski University of Bordeaux I, Talence, France Available Formats:  Softcover ISBN: 978-0-8218-5265-1 Product Code: SURV/93.S  List Price:$108.00 MAA Member Price: $97.20 AMS Member Price:$86.40
 Electronic ISBN: 978-1-4704-1320-0 Product Code: SURV/93.S.E
 List Price: $108.00 MAA Member Price:$97.20 AMS Member Price: $86.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$162.00 MAA Member Price: $145.80 AMS Member Price:$129.60
• Book Details

Mathematical Surveys and Monographs
Volume: 932002; 439 pp
MSC: Primary 47; 30; 93;

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.

• Part C. Model operators and free interpolation
• 1. The basic function model
• 2. Elements of spectral theory in the language of the characteristic function
• 3. Decompositions into invariant subspaces and free interpolation
• Part D. Analytic problems in linear system theory
• 1. Basic theory
• 2. First optimizations: Multiplicity of the spectrum and the DISC
• 3. Eigenvector decompositions, vector valued exponentials, and squared optimization
• 4. A glance at bases of exponentials and of reproducing kernels
• 5. A brief introduction to $H^\infty$ control
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 932002; 439 pp
MSC: Primary 47; 30; 93;

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.

• Part C. Model operators and free interpolation
• 1. The basic function model
• 2. Elements of spectral theory in the language of the characteristic function
• 3. Decompositions into invariant subspaces and free interpolation
• Part D. Analytic problems in linear system theory
• 1. Basic theory
• 2. First optimizations: Multiplicity of the spectrum and the DISC
• 3. Eigenvector decompositions, vector valued exponentials, and squared optimization
• 4. A glance at bases of exponentials and of reproducing kernels
• 5. A brief introduction to $H^\infty$ control
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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