A Functional Calculus Approach to the Ursell-Mayer Functions
C. Y. Shen · Journal of Mathematical Physics · 1972
A more complete treatment of the Ursell-Mayer functions is given here by way of a functional calculus defined on the algebra of complex-valued functions on the exponential of a set. Through measure-theoretical considerations, we are able to establish relationships between these functions and certain linear operators which relate probability densities and correlation functions in statistical mechanics. Also we point out that these functions provide a way of representing states of an infinite system.