| Description |
1 online resource (xxii, 253 pages) : illustrations |
| Series |
Encyclopedia of mathematics and its applications ; v. 10. Section, Analysis |
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Encyclopedia of mathematics and its applications ; v. 10.
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Encyclopedia of mathematics and its applications. Section, Analysis.
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| 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 |
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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 |
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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 |
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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 |
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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 |
| Notes |
Imprint and ISBN from label on title page verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley Pub. Co., Advanced Book Program, 1979 |
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Publication taken over by Cambridge University Press in 1984 with a new copyright date |
| Bibliography |
Includes bibliographical references (pages 204-213) and index |
| Notes |
Print version record |
| Subject |
Differential equations.
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Differential equations, Partial.
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Integral equations.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Differential equations
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Differential equations, Partial
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Integral equations
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Differentialgleichung
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Partielle Integration
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| Form |
Electronic book
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| Author |
Friedman, Charles N
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| ISBN |
9781461938170 |
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1461938171 |
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9781107340701 |
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1107340705 |
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9781139886109 |
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113988610X |
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