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Operators, Functions, and Systems: An Easy Reading: Volume 1: Hardy, Hankel, and Toeplitz
 
Nikolai K. Nikolski :  University of Bordeaux I, Talence, France
Operators, Functions, and Systems: An Easy Reading
Softcover ISBN:  978-0-8218-4933-0
Product Code:  SURV/92.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1319-4
Product Code:  SURV/92.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4933-0
eBook: ISBN:  978-1-4704-1319-4
Product Code:  SURV/92.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Add to cart
Operators, Functions, and Systems: An Easy Reading
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Operators, Functions, and Systems: An Easy Reading: Volume 1: Hardy, Hankel, and Toeplitz
Nikolai K. Nikolski :  University of Bordeaux I, Talence, France
Softcover ISBN:  978-0-8218-4933-0
Product Code:  SURV/92.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1319-4
Product Code:  SURV/92.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4933-0
eBook ISBN:  978-1-4704-1319-4
Product Code:  SURV/92.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Add to cart
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 92; 2002; 461 pp
    MSC: Primary 47; 30; 93

    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. Infinite-dimensional 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, Nevanlinna-Pick 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
     
     
    • Volume 1. Hardy, Hankel and Toeplitz
    • Part A. An invitation to Hardy Classes
    • 1. Invariant subspaces of $L^2(\mu )$
    • 2. First applications
    • 3. $H^p$ classes. Canonical factorization
    • 4. Szegö infimum, and generalized Phragmén–Lindelöf principle
    • 5. Harmonic analysis in $L^2(\mathbb {T},\mu )$
    • 6. Transfer to the half-plane
    • 7. Time-invariant filtering
    • 8. Distance formulae and zeros of the Riemann $\zeta $-function
    • Part B. Hankel and Toeplitz operators
    • 1. Hankel operators and their symbols
    • 2. Compact Hankel operators
    • 3. Applications to Nevanlinna–Pick interpolation
    • 4. Essential spectrum. The first step: Elements of Toeplitz operators
    • 5. Essential spectrum. The second step: The Hilbert matrix and other Hankel operators
    • 6. Hankel and Toeplitz operators associated with moment problems
    • 7. Singular numbers of Hankel operators
    • 8. Trace class Hankel operators
    • 9. Inverse spectral problems, stochastic processes and one-sided invertibility
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Mathematical Surveys and Monographs
Volume: 92; 2002; 461 pp
MSC: Primary 47; 30; 93

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. Infinite-dimensional 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, Nevanlinna-Pick 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.
  • Volume 1. Hardy, Hankel and Toeplitz
  • Part A. An invitation to Hardy Classes
  • 1. Invariant subspaces of $L^2(\mu )$
  • 2. First applications
  • 3. $H^p$ classes. Canonical factorization
  • 4. Szegö infimum, and generalized Phragmén–Lindelöf principle
  • 5. Harmonic analysis in $L^2(\mathbb {T},\mu )$
  • 6. Transfer to the half-plane
  • 7. Time-invariant filtering
  • 8. Distance formulae and zeros of the Riemann $\zeta $-function
  • Part B. Hankel and Toeplitz operators
  • 1. Hankel operators and their symbols
  • 2. Compact Hankel operators
  • 3. Applications to Nevanlinna–Pick interpolation
  • 4. Essential spectrum. The first step: Elements of Toeplitz operators
  • 5. Essential spectrum. The second step: The Hilbert matrix and other Hankel operators
  • 6. Hankel and Toeplitz operators associated with moment problems
  • 7. Singular numbers of Hankel operators
  • 8. Trace class Hankel operators
  • 9. Inverse spectral problems, stochastic processes and one-sided invertibility
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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