One-Parameter Semigroups

The theory of semigroups of operators was initiated by E. Hille in his monograph ``Functional Analysis and Semigroups'' which appeared in 1948. In the years thereafter the theory was developed further by W. Feller, T. Kato, R.S. Phillips, K. Yosida and many others. The possible range of applications is enormous and includes problems in mathematical physics, probability theory and control theory. The purpose of this book is to illustrate the richness of the theory of one-parameter semigroups by examining some of its various aspects. It is written in such a way that all three parts can be read more or less independently; it is assumed that the reader is familiar with some of the basic principles of functional analysis.