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The Resource Product integration with applications to differential equations, John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P.R. Masani, (electronic resource)
Product integration with applications to differential equations, John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P.R. Masani, (electronic resource)
Resource Information
The item Product integration with applications to differential equations, John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P.R. Masani, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Product integration with applications to differential equations, John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P.R. Masani, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 This 1979 book shows how differential equation theory can be beautifully simplified by treating such equations from the product integral viewpoint
 Language

 eng
 eng
 Extent
 1 online resource (288 p.)
 Note
 Description based upon print version of record
 Contents

 Cover; Half Title; Series Page; Title; Copyright; ; Contents; Editor's Statement; Foreword; Preface; Introduction; CHAPTER 1 Product Integration of MatrixValued Functions; 1.0 Introduction; 1.1 Product Integration; 1.2 Product Integral Analysis of Linear Ordinary Differential Equations; 1.3 Further Properties of Product Integrals; 1.4 Estimates of Size, and the Product Integral as a TimeOrdered Exponential; 1.5 Dependence on a Parameter; 1.6 Improper Product Integration; 1.7 Alternative Definitions of the Product Integral; 1.8 LebesgueIntegrable Functions; Notes to Chapter 1
 CHAPTER 2 Contour Product Integration2.0 Introduction; 2.1 The Definition of Contour Product Integrals; 2.2 The Product Integral of an Analytic Function and the Analogues of Cauchy's Integral Theorem; 2.3 A Cauchy Integral Formula for Product Integrals; 2.4 Generalizations; Notes to Chapter 2; CHAPTER 3 Strong Product Integration; 0. Introduction; 3.1 Direct Extensions of the Results of Chapter 1; 3.2 Generalization; 3.3 The Space; 3.4 Solution of Integral Equations; 3.5 Product Integration of Functions in Ls1(a,b); 3.6 Product Integrals Involving Unbounded Operators; Notes to Chapter 3
 CHAPTER 4 Applications4.1 Asymptotics for the Schrödinger Equation; 4.2 Weyl's LimitCircle Classification; 4.3 The Lie Product Formula; 4.4 The HilleYosida Theorem; 4.5 An Example Involving Unbounded Operators with Variable Domain; Notes to Chapter 4; CHAPTER 5 Product Integration of Measures; 5.1. Introduction; 5.2 The Product Integral; 5.3 Integral and Differential Equations; 5.4 Further Properties of Product Integrals; 5.5 Improper Product Integration; 5.6 The Schrödinger Equation; 5.7 The Equation y""+p(dx)y' + q(dx)y = 0; Notes to Chapter 5; CHAPTER 6 Complements
 other Work and further Results on Product IntegrationAPPENDIX I; APPENDIX I Matrices; A.I.I Elementary Definitions; A.I.2 Calculus of CnxnValued Functions; A.I.3 The Canonical Form of a Matrix; A.I.4 The Spectrum of a Matrix; A.I.5 Some Additional Results; References; Notes to the References; APPENDIX II; APPENDIX II The Place of Multiplicative Integration in Modern Analysis*; A.II.2 Fluid Flows in Smooth Manifolds; A. Linear Manifolds; B. Nonlinear Manifolds; C. Steady Flows; A.II.3 Abstract Formulation of the Theory; A.II.4 The Evolution Equation in a Pseudolinear Algebra
 A.II.5 LinearizationA.II.6 DiscreteState Markovian Processes with Continuous Time Domain; A.II.7 The Monodromy and Cousin Problems; A.II.8 The Matricial Hardy and Nevanlinna Classes; A.II.9 Holonomy; A.II.10 Perturbation and Partial Integration; A.II.ll Concluding Remarks; References; Index
 Isbn
 9781107387195
 Label
 Product integration with applications to differential equations
 Title
 Product integration with applications to differential equations
 Statement of responsibility
 John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P.R. Masani
 Language

 eng
 eng
 Summary
 This 1979 book shows how differential equation theory can be beautifully simplified by treating such equations from the product integral viewpoint
 Cataloging source
 MiAaPQ
 http://library.link/vocab/creatorName
 Dollard, John D
 Dewey number

 515.3
 515.352
 Index
 index present
 Language note
 English
 LC call number
 QA371
 LC item number
 .D64 1979
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Friedman, Charles N
 Series statement

 Encyclopedia of mathematics and its applications
 Encyclopedia of Mathematics and its Applications
 Series volume
 v. 10
 http://library.link/vocab/subjectName

 Differential equations
 Differential equations, Partial
 Integral equations
 Label
 Product integration with applications to differential equations, John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P.R. Masani, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 204213) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Cover; Half Title; Series Page; Title; Copyright; ; Contents; Editor's Statement; Foreword; Preface; Introduction; CHAPTER 1 Product Integration of MatrixValued Functions; 1.0 Introduction; 1.1 Product Integration; 1.2 Product Integral Analysis of Linear Ordinary Differential Equations; 1.3 Further Properties of Product Integrals; 1.4 Estimates of Size, and the Product Integral as a TimeOrdered Exponential; 1.5 Dependence on a Parameter; 1.6 Improper Product Integration; 1.7 Alternative Definitions of the Product Integral; 1.8 LebesgueIntegrable Functions; Notes to Chapter 1
 CHAPTER 2 Contour Product Integration2.0 Introduction; 2.1 The Definition of Contour Product Integrals; 2.2 The Product Integral of an Analytic Function and the Analogues of Cauchy's Integral Theorem; 2.3 A Cauchy Integral Formula for Product Integrals; 2.4 Generalizations; Notes to Chapter 2; CHAPTER 3 Strong Product Integration; 0. Introduction; 3.1 Direct Extensions of the Results of Chapter 1; 3.2 Generalization; 3.3 The Space; 3.4 Solution of Integral Equations; 3.5 Product Integration of Functions in Ls1(a,b); 3.6 Product Integrals Involving Unbounded Operators; Notes to Chapter 3
 CHAPTER 4 Applications4.1 Asymptotics for the Schrödinger Equation; 4.2 Weyl's LimitCircle Classification; 4.3 The Lie Product Formula; 4.4 The HilleYosida Theorem; 4.5 An Example Involving Unbounded Operators with Variable Domain; Notes to Chapter 4; CHAPTER 5 Product Integration of Measures; 5.1. Introduction; 5.2 The Product Integral; 5.3 Integral and Differential Equations; 5.4 Further Properties of Product Integrals; 5.5 Improper Product Integration; 5.6 The Schrödinger Equation; 5.7 The Equation y""+p(dx)y' + q(dx)y = 0; Notes to Chapter 5; CHAPTER 6 Complements
 other Work and further Results on Product IntegrationAPPENDIX I; APPENDIX I Matrices; A.I.I Elementary Definitions; A.I.2 Calculus of CnxnValued Functions; A.I.3 The Canonical Form of a Matrix; A.I.4 The Spectrum of a Matrix; A.I.5 Some Additional Results; References; Notes to the References; APPENDIX II; APPENDIX II The Place of Multiplicative Integration in Modern Analysis*; A.II.2 Fluid Flows in Smooth Manifolds; A. Linear Manifolds; B. Nonlinear Manifolds; C. Steady Flows; A.II.3 Abstract Formulation of the Theory; A.II.4 The Evolution Equation in a Pseudolinear Algebra
 A.II.5 LinearizationA.II.6 DiscreteState Markovian Processes with Continuous Time Domain; A.II.7 The Monodromy and Cousin Problems; A.II.8 The Matricial Hardy and Nevanlinna Classes; A.II.9 Holonomy; A.II.10 Perturbation and Partial Integration; A.II.ll Concluding Remarks; References; Index
 Dimensions
 unknown
 Extent
 1 online resource (288 p.)
 Form of item
 online
 Isbn
 9781107387195
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (CKB)2670000000361540
 (EBL)1543496
 (OCoLC)862614416
 (SSID)ssj0000890260
 (PQKBManifestationID)11467957
 (PQKBTitleCode)TC0000890260
 (PQKBWorkID)10883151
 (PQKB)10168284
 (UkCbUP)CR9781107340701
 (MiAaPQ)EBC1543496
 (EXLCZ)992670000000361540
 Label
 Product integration with applications to differential equations, John D. Dollard and Charles N. Friedman ; foreword by Felix E. Browder ; appendix by P.R. Masani, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 204213) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Cover; Half Title; Series Page; Title; Copyright; ; Contents; Editor's Statement; Foreword; Preface; Introduction; CHAPTER 1 Product Integration of MatrixValued Functions; 1.0 Introduction; 1.1 Product Integration; 1.2 Product Integral Analysis of Linear Ordinary Differential Equations; 1.3 Further Properties of Product Integrals; 1.4 Estimates of Size, and the Product Integral as a TimeOrdered Exponential; 1.5 Dependence on a Parameter; 1.6 Improper Product Integration; 1.7 Alternative Definitions of the Product Integral; 1.8 LebesgueIntegrable Functions; Notes to Chapter 1
 CHAPTER 2 Contour Product Integration2.0 Introduction; 2.1 The Definition of Contour Product Integrals; 2.2 The Product Integral of an Analytic Function and the Analogues of Cauchy's Integral Theorem; 2.3 A Cauchy Integral Formula for Product Integrals; 2.4 Generalizations; Notes to Chapter 2; CHAPTER 3 Strong Product Integration; 0. Introduction; 3.1 Direct Extensions of the Results of Chapter 1; 3.2 Generalization; 3.3 The Space; 3.4 Solution of Integral Equations; 3.5 Product Integration of Functions in Ls1(a,b); 3.6 Product Integrals Involving Unbounded Operators; Notes to Chapter 3
 CHAPTER 4 Applications4.1 Asymptotics for the Schrödinger Equation; 4.2 Weyl's LimitCircle Classification; 4.3 The Lie Product Formula; 4.4 The HilleYosida Theorem; 4.5 An Example Involving Unbounded Operators with Variable Domain; Notes to Chapter 4; CHAPTER 5 Product Integration of Measures; 5.1. Introduction; 5.2 The Product Integral; 5.3 Integral and Differential Equations; 5.4 Further Properties of Product Integrals; 5.5 Improper Product Integration; 5.6 The Schrödinger Equation; 5.7 The Equation y""+p(dx)y' + q(dx)y = 0; Notes to Chapter 5; CHAPTER 6 Complements
 other Work and further Results on Product IntegrationAPPENDIX I; APPENDIX I Matrices; A.I.I Elementary Definitions; A.I.2 Calculus of CnxnValued Functions; A.I.3 The Canonical Form of a Matrix; A.I.4 The Spectrum of a Matrix; A.I.5 Some Additional Results; References; Notes to the References; APPENDIX II; APPENDIX II The Place of Multiplicative Integration in Modern Analysis*; A.II.2 Fluid Flows in Smooth Manifolds; A. Linear Manifolds; B. Nonlinear Manifolds; C. Steady Flows; A.II.3 Abstract Formulation of the Theory; A.II.4 The Evolution Equation in a Pseudolinear Algebra
 A.II.5 LinearizationA.II.6 DiscreteState Markovian Processes with Continuous Time Domain; A.II.7 The Monodromy and Cousin Problems; A.II.8 The Matricial Hardy and Nevanlinna Classes; A.II.9 Holonomy; A.II.10 Perturbation and Partial Integration; A.II.ll Concluding Remarks; References; Index
 Dimensions
 unknown
 Extent
 1 online resource (288 p.)
 Form of item
 online
 Isbn
 9781107387195
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (CKB)2670000000361540
 (EBL)1543496
 (OCoLC)862614416
 (SSID)ssj0000890260
 (PQKBManifestationID)11467957
 (PQKBTitleCode)TC0000890260
 (PQKBWorkID)10883151
 (PQKB)10168284
 (UkCbUP)CR9781107340701
 (MiAaPQ)EBC1543496
 (EXLCZ)992670000000361540
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