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Schur Parameters, Factorization and Dilation Problems

Author: Tiberiu Constantinescu
Publisher: Basel : Birkhäuser Basel, 1995.
Series: Operator theory, advances and applications, 82.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells. Together with the transmission line, their physical counter- part, they appear in scattering theory, in modeling, prediction and filtering of nonstationary processes, in signal processing, geophysics and system theory. Modeling problems  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tiberiu Constantinescu
ISBN: 9783034891080 3034891083 9783034899109 3034899106
OCLC Number: 840291278
Description: 1 online resource.
Contents: 1 Schur Parameters and Positive Block Matrices --
1.1 Preliminaries --
1.2 Renorming Hilbert Spaces and Elementary Rotations --
1.3 Kolmogorov Decompositions. I --
1.4 Row and Column Contractions --
1.5 The Structure of Positive Definite Kernels --
1.6 Kolmogorov Decompositions. II --
1.7 Notes --
2 Models for Triangular Contractions --
2.1 Preliminaries --
2.2 The Structure of Triangular Contractions --
2.3 Realization of Triangular Contractions --
2.4 Unitary Couplings and Operator Ranges --
2.5 Modeling Families of Contractions --
2.6 Notes --
3 Moment Problems and Interpolation --
3.1 A Survey on Completion Problems --
3.2 Extensions of Partial Isometries --
3.3 Krein's Formula --
3.4 Moment Problems --
3.5 The Commutant Lifting Method --
3.6 Notes --
4 Displacement Structures --
4.1 Structured Matrices --
4.2 Generalized Schur Algorithm --
4.3 Discrete Transmission-Line Models --
4.4 Displacement Structure and Completion Problems --
4.5 Other Applications --
4.6 Notes --
5 Factorization of Positive Definite Kernels --
5.1 Spectral Factors --
5.2 Examples --
5.3 Schur's Algorithm, Szegö's Theory and Spectral Factors --
5.4 Maximum Entropy --
5.5 Notes --
6 Nonstationary Processes --
6.1 Modeling Nonstationary Processes --
6.2 Kolmogorov-Wiener Prediction --
6.3 Other Prediction Problems --
6.4 Szegö's Limit Theorems --
6.5 Notes --
7 Graphs and Completion Problems --
7.1 Preliminaries --
7.2 Completing Positive Partial Matrices. I --
7.3 Completing Positive Partial Matrices. II --
7.4 Completing Contractive Partial Matrices --
7.5 Notes --
8 Determinantal Formulae and Optimization --
8.1 Determinantal Formulae --
8.2 Maximum Determinant Formulae --
8.3 Maximum Determinant for Nonchordal Graphs --
8.4 Inheritance Principles --
8.5 Notes --
References.
Series Title: Operator theory, advances and applications, 82.
Responsibility: by Tiberiu Constantinescu.

Abstract:

This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells. Together with the transmission line, their physical counter- part, they appear in scattering theory, in modeling, prediction and filtering of nonstationary processes, in signal processing, geophysics and system theory. Modeling problems are considered for certain classes of operators, interpolation problems, determinental formulae, as well as connections with certain classes of graphs where, again, the Schur parameters could play a role. Some general algorithms that explore the transmission line are also presented in this book. As a whole, the text is self-contained and it is addressed to people interested in the previously mentioned topics or connections between them.

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