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The Schur Algorithm, Reproducing Kernel Spaces and System Theory
 
Daniel Alpay Ben-Gurion University of the Negev, Beer-sheva, Israel
A co-publication of the AMS and the Société Mathématique de France
The Schur Algorithm, Reproducing Kernel Spaces and System Theory
Softcover ISBN:  978-0-8218-2155-8
Product Code:  SMFAMS/5
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $54.40
The Schur Algorithm, Reproducing Kernel Spaces and System Theory
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The Schur Algorithm, Reproducing Kernel Spaces and System Theory
Daniel Alpay Ben-Gurion University of the Negev, Beer-sheva, Israel
A co-publication of the AMS and the Société Mathématique de France
Softcover ISBN:  978-0-8218-2155-8
Product Code:  SMFAMS/5
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $54.40
  • Book Details
     
     
    SMF/AMS Texts and Monographs
    Volume: 52001; 150 pp
    MSC: Primary 46; 93;

    The class of Schur functions consists of analytic functions on the unit disk that are bounded by \(1\). The Schur algorithm associates to any such function a sequence of complex constants, which is much more useful than the Taylor coefficients. There is a generalization to matrix-valued functions and a corresponding algorithm. These generalized Schur functions have important applications to the theory of linear operators, to signal processing and control theory, and to other areas of engineering.

    In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. The inverse scattering problem plays a key role in the exposition. The point of view also allows for a natural way to tackle more general cases, such as nonstationary systems, non-positive metrics, and pairs of commuting nonself-adjoint operators. This is the English translation of a volume originally published in French by the Société Mathématique de France. Translated by Stephen S. Wilson.

    Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

    Readership

    Graduate students and pure and applied research mathematicians interested in functional analysis, systems theory, and control.

  • Reviews
     
     
    • From a review of the French edition:

      This excellent survey showing a rich interplay between functional analysis, complex analysis and systems science is very informative and can be highly recommended to functional analysts curious about the systems science impact of their discipline or to theoretically inclined systems scientists, in particular those involved in the realization theory.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 52001; 150 pp
MSC: Primary 46; 93;

The class of Schur functions consists of analytic functions on the unit disk that are bounded by \(1\). The Schur algorithm associates to any such function a sequence of complex constants, which is much more useful than the Taylor coefficients. There is a generalization to matrix-valued functions and a corresponding algorithm. These generalized Schur functions have important applications to the theory of linear operators, to signal processing and control theory, and to other areas of engineering.

In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. The inverse scattering problem plays a key role in the exposition. The point of view also allows for a natural way to tackle more general cases, such as nonstationary systems, non-positive metrics, and pairs of commuting nonself-adjoint operators. This is the English translation of a volume originally published in French by the Société Mathématique de France. Translated by Stephen S. Wilson.

Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

Readership

Graduate students and pure and applied research mathematicians interested in functional analysis, systems theory, and control.

  • From a review of the French edition:

    This excellent survey showing a rich interplay between functional analysis, complex analysis and systems science is very informative and can be highly recommended to functional analysts curious about the systems science impact of their discipline or to theoretically inclined systems scientists, in particular those involved in the realization theory.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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