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)

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
Creator
Contributor
Subject
Genre
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
Member of
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)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 204-213) 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 Matrix-Valued 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 Time-Ordered Exponential; 1.5 Dependence on a Parameter; 1.6 Improper Product Integration; 1.7 Alternative Definitions of the Product Integral; 1.8 Lebesgue-Integrable 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 Limit-Circle Classification; 4.3 The Lie Product Formula; 4.4 The Hille-Yosida 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 Cnxn-Valued 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 Discrete-State 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)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 204-213) 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 Matrix-Valued 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 Time-Ordered Exponential; 1.5 Dependence on a Parameter; 1.6 Improper Product Integration; 1.7 Alternative Definitions of the Product Integral; 1.8 Lebesgue-Integrable 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 Limit-Circle Classification; 4.3 The Lie Product Formula; 4.4 The Hille-Yosida 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 Cnxn-Valued 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 Discrete-State 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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