Fourier–Feynman transforms and Wiener integrals in the Fresnel class on abstract Wiener spaces

Abstract

The purpose of this article is to establish some relationships between L ₁-analytic Fourier–Feynman transforms

and Wiener integrals for certain bounded functions F in the Fresnel class ℱ(B) of the form: F(x) = ∫ _H exp{i(h, x)^∼}dμ(h), μ ∈ M(H), on the abstract Wiener space.

Keywords:

• Abstract Wiener space
• Wiener integral
• Fourier–Feynman transform
• Fresnel class