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
