Semigroups of Linear Operators and Applications: Second Edition

by Jerome A. Goldstein

Overview

This advanced monograph of semigroup theory explores semigroups of linear operators and linear Cauchy problems. Suitable for graduate students in mathematics as well as professionals in science and engineering, the treatment begins with an introductory survey of the theory and applications of semigroups of operators. Two main sections follow, one dedicated to semigroups of linear operators, and the other to linear Cauchy problems.
Author Jerome A. Goldstein emphasizes motivation and heuristics as well as applications. Each of the two sections concludes with further applications and historical notes. Challenging exercises appear throughout the text, which includes a substantial bibliography. This edition has been updated with supplementary transcripts of five lectures given by the author during a 1989 workshop at Blaubeuren, Germany.

Product Details

ISBN-13:	9780486812571
Publisher:	Dover Publications
Publication date:	05/17/2017
Series:	Dover Books on Mathematics
Pages:	320
Product dimensions:	5.90(w) x 9.10(h) x 0.70(d)

About the Author

Jerome A. Goldstein is Professor of Mathematics at the University of Memphis.

Table of Contents

Chapter 0 A Heuristic Survey of the Theory and Applications of Semigroups of Operators 3

Chapter 1 Semigroups of Linear Operators 13

1 Notation; Closed Operators 13

2 The Hille-Yosida Generation Theorem 14

3 Dissipative Operators: The Hille-Yosida Theorem Again 25

4 Adjoint Semigroups; Stone's Theorem 30

5 Analytic Semigroups 33

6 Perturbation Theory 38

7 Approximation Theory 44

8 Some Applications 48

9 Further Developments and Applications 61

10 Historical Notes and Remarks 78

Chapter 2 Linear Cauchy Problems 83

1 Homogeneous and Inhomogeneous Equations 83

2 Nonlinear Equations 87

3 Fourier Transforms, Partial Differential Operators, and unitary Equivalence 92

4 Parabolic Equations 95

5 Regularity for Parabolic Problems 98

6 The Spectral Theorem 101

7 Second-Order Equations 110

8 Cosine Functions 118

9 Symmetric Hyperbolic Systems 121

10 Higher Order Equations 125

11 Singular Perturbations 128

12 Mixed Problems 134

13 Time Dependent Equations 140

14 Scattering Theory 147

15 Further Applications 160

16 Historical Notes and Remarks 176

References 181

Transcripts of Five Lectures Given by the Author at a 1989 Workshop in Blaubeuren, Germany 232

Participants from the 1989 Blaubeuren Workshop 234

1 On Hardy-Landau-Littlewood Inequalities 236

2 The Feynman-Kac Formula with an Application to the Heat Equation with a Singular Potential 247

3 Scattering Theory and Equipartition of Energy 262

4 The Navier-Stokes Equations 274

5 Singular Perturbation 284

Index of Symbols 296

Author Index 299

Subject Index 306