《正则半群和非椭圆微分算子》编著者Zheng Quan、Li Miao。

本书系统介绍了近二十年来算子半群理论尤其是正则算子半群对非椭圆偏微分算子的应用。前两章详细介绍正则半群的基本理论，包括扰动、逼近、表示以及与抽象Cauchy问题的关系等。第三章介绍了积分半群的基本性质，以及积分半群和正则半群的关系。第四章和第五章分别给出了半群理论对常系数抽象微分算子和偏微分算子的应用，对比了用正则半群和积分半群所得结果，表明了正则半群是处理非椭圆偏微分算子的适当工具。第六章介绍了正则半群对时变系数非椭圆微分算子的应用。第七章介绍了正则半群对抛物系统、恰当系统和双曲系统的应用。第八章介绍了正则半群对Schr?dinger算子的应用。

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