Generators of strongly continuous semigroups

by J. A. van Casteren

This research note contains some recent results in the theory of strongly continuous semigroups of linear operators. Topics covered include the Feynman-Kac formalism with applications to Schrödinger operators, positivity preserving semigroups, quadratic form theory, holomorphic semigroups and bounded one-parameter groups. An appendix deals with some aspects of Feynman path integrals. A number of previously inaccessible results in semigroup theory are presented with full proofs. This work will be useful both for those undertaking research as well as for graduate students; a basic knowledge of functional analysis and probability theory are the only prerequisites.