UID:
edocfu_9959233517202883
Umfang:
1 online resource (xxii, 253 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88610-X
,
1-107-38358-7
,
1-299-82066-2
,
1-107-39481-3
,
1-4619-3817-1
,
1-107-39002-8
,
1-107-39844-4
,
1-107-38719-1
,
1-107-34070-5
Serie:
Encyclopedia of mathematics and its applications ;
Inhalt:
Originally published in 1979, this book shows the beautiful simplifications that can be brought to the theory of differential equations by treating such equations from the product integral viewpoint. The first chapter of the book, dealing with linear ordinary differential equations, should be accessible to anyone with a knowledge of matrix theory and elementary calculus. Later chapters assume more sophistication on the part of the reader. The essential unity of these subjects is illustrated by the fact that the idea of the product integral can be naturally and effectively used to deal with all of them.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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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
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English
Weitere Ausg.:
ISBN 0-521-17737-5
Weitere Ausg.:
ISBN 0-521-30230-7
Sprache:
Englisch
