本書系統介紹了近二十年來算子半群理論尤其是正則算子半群對非橢圓偏微分算子的應用。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問題的關系等。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系。第四章和第五章分別給出了半群理論對常系數抽象微分算子和偏微分算子的應用，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算子的適當工具。第六章介紹了正則半群對時變系數非橢圓微分算子的應用。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應用。第八章介紹了正則半群對Schr?dinger算子的應用。

Chapter 1 Regularized Semigroups1.1 Definitions and properties1.2 Generation theorems1.3 Interpolation and extrapolation1.4 Classes of regularized semigroups1.5 Relationship to abstract Cauchy problems1.6 NotesChapter 2 Perturbations, Approximations and Representations...2.1 Perturbation theorems2.2 Approximation theorems2.3 Representation and product formulas2.4 Regularized cosine functions2.5 NotesChapter 3 Integrated Semigroups3.1 Properties and characterizations3.2 Perturbations of integrated semigroups3.3 Relationship to regularized semigroups3.4 NotesChapter 4 Abstract Differential Operators with Constant Coefficients4.1 A functional calculus4.2 Strongly and weakly elliptic operators4.3 Coercive operators4.4 Operators with coercive real parts4.5 NotesChapter 5 Applications to Partial Differential Operators-..5.1 General results5.2 Special cases and examples5.3 Resolvent sets and hypoelliptic operators5.4 Comparison of results5.5 NotesChapter 6 Abstract Differential Operators with Time-dependentCoefficients6.1 Evolution families6.2 Evolution equations6.3 Applications to partial differential equations6.4 NotesChapter 7 Parabolic~ Correct and Hyperbolic Systems7.1 Parabolic and correct systems7.2 Parabolic and correct systems: continue7.3 Hyperbolic systems7.4 NotesChapter 8 SchrSdinger Equations8.1 Convex hypersurfaces of finite type8.2 Lp-Lq estimates for free Schrodinger equations8.3 Lp estimates for SchrSdinger equations8.4 Notes and CommentsBibliographyAppendix A Vector-valued Laplace TransformsAppendix B Fractional Power of Closed OperatorsAppendix C Fourier MultipliersAppendix D C0-semigroupsList of Symbols and AbbreviationsIndex