Analytic Feynman integrals, Fourier–Feynman transforms and change of scale formula for Wiener integrals over paths on abstract Wiener spaces

Abstract

We establish the analytic Wiener and Feynman integral theory for Wiener integrals over paths on C 0 (B), the space of abstract Wiener space valued continuous functions on [0, T], for certain cylinder-type functions of the form: where f ∈ L p (R mn ), 1 ≤ p ≤ ∞, and 0 = s 0 ≤ s 1 ≤ · · · ≤ s n = T is a partition of [0, T]. In addition, we establish some relationships between analytic Feynman integrals, Fourier–Feynman transforms and Wiener integrals and we prove the change of scale formula for Wiener integrals over paths on C 0 (B) in abstract Wiener spaces.