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SMF/AMS Texts and Monographs - Titles - 5 (2001)

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The Schur Algorithm, Reproducing Kernel Spaces and System Theory
Publié en français dans le numéro 6 (1998) de la revue Panoramas et synthèses
Daniel Alpay
Société Mathématique de France et AmericanMathematical Society
SMF/AMS Texts and Monographs 5 (2001), viii+150 pages
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Abstract:
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 causes, such as nonstationary systems, nonpositive metrics, and pairs of commuting nonself-adjoint operators.

Class. math. : 46-E-22, 93-02


ISSN : 1525-2302