From the reviews Since E. Hille and K. Yoshida established thecharacterization of generators of C0 semigroups in the 1940s semigroups oflinear operators and its... » 

From the reviews Since E. Hille and K. Yoshida established thecharacterization of generators of C0 semigroups in the 1940s semigroups oflinear operators and its neighboring areas have developed into a beautifulabstract theory. Moreover the fact that mathematically this abstract theoryhas many direct and important applications in partial differential equationsenhances its importance as a necessary discipline in both functional analysisand differential equations. In my opinion Pazy has done an outstanding job inpresenting both the abstract theory and basic applications in a clear andinteresting manner. The choice and order of the material the clarity of theproofs and the overall presentation make this an excellent place for bothresearchers and students to learn about C0 semigroups. Bulletin AppliedMathematical Sciences 4851 In spite of the other monographs on the subjectthe reviewer can recommend that of Pazy as being particularly written with abias noticeably different from that of the other volumes. Pazys decision togive a connected account of the applications to partial differential equationsin the last two chapters was a particularly happy one since it enables one tosee what the theory can achieve much better than would the insertion ofoccasional examples. The chapters achieve a very nice balance between being soeasy as to appear disappointing and so sophisticated that they areincomprehensible except to the expert. Bulletin of the London MathematicalSociety2 «