This book provides an introduction the propagator theory. Propagators are two-parameter families of linear operators, also known as evolution operators, evolutions families, non-autonomous sernigroups, etc., which are often used as mathematical models of a system evolving in a changing environment. Although this book concerns such diverse subjects as analysis, semigroup theory, probability theory, mathematical physics, and partial differential equations, it is unified by the Feynman-Kac propagator which describes the evolution of a physical system in the presence of time-dependent absorption...
This book provides an introduction the propagator theory. Propagators are two-parameter families of linear operators, also known as evolution operator...
In this book, a beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. The unified approach provides a new viewpoint of and a deeper insight into the subject.
In this book, a beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theo...
