目录
- Contents
Chapter 1 Regularized Semigroups 1
1.1 Definitions and properties 1
1.2 Generation theorems 7
1.3 Interpolation and extrapolation 13
1.4 Classes of regularized semigroups 17
1.5 Relationship to abstract Cauchy problems 23
1.6 Notes 28
Chapter 2 Perturbations,Approximations and Representations 30
2.1 Perturbation theorems 30
2.2 Approximation theorems 36
2.3 Representation and product formulas 41
2.4 Regularized cosine functions 46
2.5 Notes 53
Chapter 3 Integrated Semigroups 55
3.1 Properties and characterizations 55
3.2 Perturbations of integrated semigroups 61
3.3 Relationship to regularized semigroups 66
3.4 Notes 71
Chapter 4 Abstract Differential Operators with Constant Coefficients 74
4.1 A functional calculus 74
4.2 Strongly and weakly elliptic operators 79
4.3 Coercive operators 86
4.4 Operators with coercive real parts 92
4.5 Notes 96
Chapter 5 Applications to Partial Differential Operators 97
5.1 General results 97
5.2 Special cases and examples 101
5.3 Resolvent sets and hypoelliptic operators 105
5.4 Comparison of results 111
5.5 Notes 116
Chapter 6 Abstract Differential Operators with Time-dependent Coefficients 118
6.1 Evolution families 118
6.2 Evolution equations 126
6.3 Applications to partial differential equations 135
6.4 Notes 141
Chapter 7 Parabolic,Correct and Hyperbolic Systems 142
7.1 Parabolic and correct systems 142
7.2 Parabolic and correct systems: continue 150
7.3 Hyperbolic systems 156
7.4 Notes 160
Chapter 8 Schrodinger Equations 162
8.1 Convex hypersurfaces of finite type 162
8.2 Lp-Lq estimates for free Schrodinger equations 167
8.3 Lp estimates for Schrodinger equations 175
8.4 Notes and Comments 178
Bibliography 181
Appendix A Vector-valued Laplace Transforms 196
Appendix B Fractional Power of Closed Operators 200
Appendix C Fourier Multipliers 202
Appendix D C0-semigroups 205
List of Symbols and Abbreviations 210
Index 212
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