A State Space Approach to Canonical Factorization with Applications

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.