The main subject of the book can be looked at from various points of view. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the point of view of probability theory, the authors are concerned with the analysis of singular Markov processes; and from the viewpoint of mathematical physics, the dynamics of equilibrium systems in quantum statistical physics and quantum field theory is analysed. The authors describe two new approaches to the subject, which have not been previously treated in monographs. The book also contains necessary background material, which makes it accessible and useful to researchers and graduate students working in functional analysis, probability, and mathematical physics.