The evolution of operator semigroups


By the early 1950s the theory of one-parameter semigroups of bounded linear operators on Banach spaces was established, and much further theory and diverse applications to many areas of mathematics and science developed rapidly. The theory was based on two main results, the wellposedness theorem and the generation theorem. By the early 1970s, analogues of these two theorems were developed for semigroups of nonlinear operators. Since then, extensions of the theory and deep and sometimes unexpected applications have continued to arise in a consistent and frequent pattern. This continues to blossom today, and a selection of these results is surveyed here.

Publication Title

Springer Proceedings in Mathematics and Statistics