《正則半群和非橢圓微分運算元（英文版）》系統介紹了近二十年來運算元半群理論尤其是正則運算元半群對非橢圓偏微分運算元的套用。前兩章詳細介紹正則半群的基本理論，包括擾動、逼近、表示以及與抽象Cauchy問題的關係等。第三章介紹了積分半群的基本性質，以及積分半群和正則半群的關係。第四章和第五章分別給出了半群理論對常係數抽象微分運算元和偏微分運算元的套用，對比了用正則半群和積分半群所得結果，表明了正則半群是處理非橢圓偏微分運算元的適當工具。第六章介紹了正則半群對時變係數非橢圓微分運算元的套用。第七章介紹了正則半群對拋物系統、恰當系統和雙曲系統的套用。第八章介紹了正則半群對Schr?dinger運算元的套用。
基本介紹
- 書名：正則半群和非橢圓微分運算元
- 作者：鄭權 李淼
- 出版日期：2014年3月1日
- 語種：簡體中文, 英語
- 品牌：科學出版社
- 外文名：Regularized Semigroups and Non-Elliptic Differential Operators
- 出版社：科學出版社
- 頁數：211頁
- 開本：5
內容簡介,圖書目錄,
內容簡介
《正則半群和非橢圓微分運算元(英文版)》由科學出版社出版。
圖書目錄
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
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
