A Series Approximation for the Analytic Fourier–Feynman Transform on Wiener Space

Abstract

In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out easy an calculation for the analytic Fourier–Feynman transform of the functionals. Some examples are furnished to illustrate the usefulness of the evaluation formula. Finally, using the evaluation formula, we establish the series approximation for the analytic Fourier–Feynman transform.

Keywords

• evaluation formula
• unbounded functionals
• analytic Fourier–Feynman transform
• series approximation