| Document Type
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BL
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| Record Number
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982564
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b736934
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| Title & Author
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A state space approach to canonical factorization with applications /\ Harm Bart [and others].
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| Publication Statement
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Basel :: Birkhäuser,, ©2010.
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| Series Statement
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Operator Theory: Advances and Applications, Linear Operators and Linear Systems ;; 200
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| Page. NO
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1 online resource (xii, 423 pages) :: illustrations
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| ISBN
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1283076306
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: 3764387521
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: 376438753X
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: 9781283076302
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: 9783764387525
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: 9783764387532
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Cover -- Table of Contents -- Preface -- Chapter 0 Introduction -- Part I Convolution Equations, Canonical Factorization and the State Space Method -- Chapter 1 The Role of Canonical Factorization in Solving Convolution Equations -- 1.1 Wiener-Hopf Integral Equations and Factorization -- 1.2 Block Toeplitz Equations and Factorization -- 1.3 Singular Integral Equations and Factorization -- Notes -- Chapter 2 The State Space Method and Factorization -- 2.1 Preliminaries on Realization -- 2.2 Realization of Rational Matrix Functions -- 2.3 Realization of Analytic Operator Functions -- 2.4 Inversion -- 2.5 Products -- 2.6 Factorization -- Notes -- Part II Convolution Equations With Rational Matrix Symbols -- Chapter 3 Explicit Solutions Using Realizations -- 3.1 Canonical Factorization of Rational Matrix Functions in State Space Form -- 3.2 Wiener-Hopf Integral Operators -- 3.3 Block Toeplitz Operators -- 3.4 Singular Integral Equations -- 3.5 The Riemann-Hilbert Boundary Value Problem -- Notes -- Chapter 4 Factorization of Non-Proper Rational Matrix Functions -- 4.1 Preliminaries About Matrix Pencils -- 4.2 Realization of a Non-Proper Rational Matrix Function -- 4.3 Explicit Canonical Factorization -- 4.4 Inversion of Singular Operators With a Rational Matrix Symbol -- 4.5 The Riemann-Hilbert Boundary Value Problem Revisited (1) -- Notes -- Part III Equations With Non-Rational Symbols -- Chapter 5 Factorization of Matrix Functions Analytic in a Strip -- 5.1 Exponentially Dichotomous Operators and Bisemigroups -- 5.2 Spectral Splitting and Proof of Theorem 5.2 -- 5.3 Realization Triples -- 5.4 Construction of Realization Triples -- 5.5 Inverting Matrix Functions Analytic in a Strip -- 5.6 Inverting Full Line Convolution Operators -- 5.7 Inverting Wiener-Hopf Integral Operators -- 5.8 Explicit Canonical Factorization -- 5.9 The Riemann-Hilbert Boundary Value Problem Revisited (2) -- Notes -- Chapter 6 Convolution Equations and the Transport Equation -- 6.1 The Transport Equation -- 6.2 The Case of a Finite Number of Scattering Directions -- 6.3 Wiener-Hopf Equations With Operator-Valued Kernel Functions -- 6.4 Construction of a Canonical Factorization -- 6.5 The Matching of the Subspaces -- 6.6 Formulas for Solutions -- Notes -- Chapter 7 Wiener-Hopf Factorization and Factorization Indices -- 7.1 Canonical Factorization of Operator Functions -- 7.2 Proof of Theorem 7.2 -- 7.3 Wiener-Hopf Factorization and Spectral Invariants -- Notes -- Part IV Factorization of Selfadjoint Rational Matrix Functions -- Chapter 8 Preliminaries Concerning Minimal Factorization -- 8.1 Minimal Realizations -- 8.2 Minimal Factorization -- 8.3 Pseudo-Canonical Factorization -- Notes -- Chapter 9 Factorization of Positive Definite Rational Matrix Functions -- 9.1 Preliminaries on Selfadjoint Rational Matrix Functions -- 9.2 Spectral Factorization -- 9.3 Positive Definite Functions on the Unit Circle -- Notes -- Chapter 10 Pseudo-Spectral Factorizations of Selfadjoint Rational Matrix Functions -- 10.1 Nonnegative Rational Matrix Functions -- 10.2 Selfadjoint Rational Matrix Functions and Further Generalization.
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| Abstract
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The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations. A large part the book deals with rational matrix functions only.
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| Subject
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Factorization of operators.
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Operator theory.
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State-space methods.
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Factorization of operators.
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| Subject
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Operator theory.
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| Subject
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State-space methods.
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| Dewey Classification
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515.724
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| LC Classification
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QA329.S73 2010
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| Added Entry
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Bart, H., (Harm),1942-
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