Semigroups and Their Generators

This chapter is a prelude. It contains a brief account of some basic notions and facts from the theory of strongly continuous semigroups of operators ( \(C_0\) -semigroups) and their generators. We also introduce here notations and definitions indispensable in the following chapters. Further, we focus here on some special classes of semigroups important for entire of our further presentation. After definition of the strongly continuous exponential function, we consider contraction and quasi-bounded semigroups, emphasising the holomorphic semigroups.