A BANACH ALGEBRA OF SERIES OF FUNCTIONS OVER PATHS

Let C[0; T] denote the space of continuous real-valued functions on [0; T]. On the space C[0; T], we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes transforms of measures of finite variation on the product of simplex and Euclidean space. We evaluate analytic Feynman integrals of the functions in the Banach algebra which play significant roles in the Feynman integration theory and quantum mechanics.