A linear transformation theorem for analytic Feynman integrals

The behavior of the analytic Feynman integral under translation has been studied in the recent work of R. H. Cameron and D. A. Storvick.The purpose of this paper is to continue the development of this transformation theory.In particular, the behavior of the analytic Feynman integral under certain linear transformations is determined and, using this linear transformation theory, a "generalized Schroedinger equation" is solved in terms of an analytic Feynman integral.2* Preliminaries* The analytic Wiener and analytic Feynman integrals were defined in [4] and [6] as follows:DEFINITION 2.1.Let the complex number λ 0 satisfy Be\ 0 ^ 0 and λ 0 Φ 0, so that λ 0 = I λ 0 1 exp (i#) for some θ on the interval [π/2, π/2].Let F(x) be a functional defined on C [a, b] (the space of continuous functions on [α, 6] which vanish at a) such that the Wiener integral J(λ) = ί F(X~hx)dx Jc7[α,&]