In the setting of Cameron and Storvick's recent theory, our main result establishes the existence of the analytic Feynman integral for functions on v-dimensional Wiener space of the form F(X) = exp {− ∝ab (A(s) X(s), X(s)) ds}. Here X is a v-valued continuous function on [a, b] such that X(a) = 0 and {A(s): a ⩽ s ⩽ b} is a commutative family of real, symmetric, positive definite matrices such that the square roots of the eigenvalues are functions of bounded variation on [a, b]. We obtain the existence theorem just referred to without having to construct special spaces, quadratic forms, etc., to fit the particular problem of interest.
