Non-Autonomous Kato Classes and Feynman-Kac Propagators

by Archil Gulisashvili, Jan A. van Casteren

This book provides an introduction to propagator theory. Propagators, or evolution families, are two-parameter analogues of semigroups of operators. Propagators are encountered in analysis, mathematical physics, partial differential equations, and probability theory. They are often used as mathematical models of systems evolving in a changing environment. A unifying theme of the book is the theory of Feynman-Kac propagators associated with time-dependent measures from non-autonomous Kato classes. In applications, a Feynman-Kac propagator describes the evolution of a physical system in the presence of time-dependent absorption and excitation. The book is suitable as an advanced textbook for graduate courses.

360 pages, Hardcover

First published July 14, 2006