Operator Semigroups: Definitions, Properties and Applications (original) (raw)

A large part of contemporary natural science is concerned with investigating the motion of systems in time with a determined state space. To conduct this investigation, we study the theory of one-parameter semigroups. The theory is developed from the simplest scalar case and finite dimensional case to semigroups of linear operators on Banach spaces which started in the first half of the last century. This thesis is designed to give a basic introduction to semigroup theory and its application. Some proofs and illustrative examples are provided. semigroups is also achieved in this chapter. In Chapter III, we will introduce one application in cell population problems. We will show how strongly continuous semigroups generate the solution to a cell equation and show that the solution is unique. It is a future goal to study spectral theory and to explore qualitative properties of strongly continuous semigroups. '•. '•. o '•. '•. i 0 A J kxk