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The Resource A state space approach to canonical factorization with applications, Harm Bart [and others]

A state space approach to canonical factorization with applications, Harm Bart [and others]

Label
A state space approach to canonical factorization with applications
Title
A state space approach to canonical factorization with applications
Statement of responsibility
Harm Bart [and others]
Contributor
Subject
Language
eng
Summary
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
Member of
Cataloging source
GW5XE
Dewey number
515.724
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA329
LC item number
.S73 2010
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1942-
http://library.link/vocab/relatedWorkOrContributorName
Bart, H.
Series statement
Operator Theory: Advances and Applications, Linear Operators and Linear Systems
Series volume
200
http://library.link/vocab/subjectName
  • Factorization of operators
  • State-space methods
  • Operator theory
  • Factorization of operators
  • Operator theory
  • State-space methods
Label
A state space approach to canonical factorization with applications, Harm Bart [and others]
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
701718755
Dimensions
unknown
Extent
1 online resource (xii, 423 pages)
Form of item
online
Isbn
9783764387525
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-7643-8753-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-7643-8752-5
Specific material designation
remote
System control number
(OCoLC)701718755
Label
A state space approach to canonical factorization with applications, Harm Bart [and others]
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
701718755
Dimensions
unknown
Extent
1 online resource (xii, 423 pages)
Form of item
online
Isbn
9783764387525
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-7643-8753-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-7643-8752-5
Specific material designation
remote
System control number
(OCoLC)701718755

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