The Schur Algorithm, Reproducing Kernel Spaces and System Theory

Released on by Daniel Alpay
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  • The Schur Algorithm, Reproducing Kernel Spaces and System Theory Book Detail

  • Author : Daniel Alpay
  • Release Date : 2001
  • Publisher : American Mathematical Soc.
  • Genre : Computers
  • Pages : 162
  • ISBN 13 : 9780821821558
  • File Size : 83,83 MB
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The Schur Algorithm, Reproducing Kernel Spaces and System Theory by Daniel Alpay PDF Summary

Book Description: 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 Societe Mathematique de France. Translated by Stephen S. Wilson.

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Reproducing Kernel Spaces and Applications

Reproducing Kernel Spaces and Applications

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The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes