正则半群和非椭圆微分算子（英文版）
作者：郑权，李淼 著
出版时间：2014年版
内容简介
In this book we report on the semigroup approach to non-elliptic differential opera- tors. which was developed in the last two decades. A detailed introduction to the theory of regularized semigroups is provided. And then we give the applications of regularized semigroups to non-elliptic differential operators with constant coeffi-cients or time-dependent coefficients， parabolic systems， correct systems， abstract differential operators and pseudo differential operators. We also give the very recent use of regularized semigroups to Schrodinger operators.
目录
Chapter 1 Regularized Semigroups
1.1 Definitions and properties
1.2 Generation theorems
1.3 Interpolation and extrapolation
1.4 Classes of regularized semigroups
1.5 Relationship to abstract Cauchy problems
1.6 Notes
Chapter 2 Perturbations, Approximations and Representations...
2.1 Perturbation theorems
2.2 Approximation theorems
2.3 Representation and product formulas
2.4 Regularized cosine functions
2.5 Notes
Chapter 3 Integrated Semigroups
3.1 Properties and characterizations
3.2 Perturbations of integrated semigroups
3.3 Relationship to regularized semigroups
3.4 Notes
Chapter 4 Abstract Differential Operators with Constant Coefficients
4.1 A functional calculus
4.2 Strongly and weakly elliptic operators
4.3 Coercive operators
4.4 Operators with coercive real parts
4.5 Notes
Chapter 5 Applications to Partial Differential Operators-..
5.1 General results
5.2 Special cases and examples
5.3 Resolvent sets and hypoelliptic operators
5.4 Comparison of results
5.5 Notes
Chapter 6 Abstract Differential Operators with Time-dependentCoefficients
6.1 Evolution families
6.2 Evolution equations
6.3 Applications to partial differential equations
6.4 Notes
Chapter 7 Parabolic Correct and Hyperbolic Systems
7.1 Parabolic and correct systems
7.2 Parabolic and correct systems: continue
7.3 Hyperbolic systems
7.4 Notes
Chapter 8 SchrSdinger Equations
8.1 Convex hypersurfaces of finite type
8.2 Lp-Lq estimates for free Schrodinger equations
8.3 Lp estimates for SchrSdinger equations
8.4 Notes and Comments
Bibliography
Appendix A Vector-valued Laplace Transforms
Appendix B Fractional Power of Closed Operators
Appendix C Fourier Multipliers
Appendix D C0-semigroups
List of Symbols and Abbreviations
Index
