Generalized Dyson Series, Generalized Feynman's Diagrams, the Feynman Integral, and Feynman's Operational Calculus

The basic purpose of the paper is to construct, for the indicated integrals, series expansions in terms of finite multiple integrals of increasing multiplicity ("generalized Dyson series''). The authors study in detail the character of these expansions in the case when the measure [lowercase Greek]Eta = [lowercase Greek]Mu + [lowercase Greek]Nu contains, in addition to a continuous part [lowercase Greek]Mu, a discrete part [lowercase Greek]Nu as well. Using generalized Feynman diagrams they give a graphical description of the expansions obtained; they also describe the Banach algebra generated by the functionals under consideration and establish connections with Feynman's operational calculus.