Analytic Fourier-Feynman transforms via the series approximation
Hyun Soo Chung
TL;DR
This paper introduces an evaluation formula for Wiener integrals on Wiener space, enabling easier computation of the analytic Fourier-Feynman transform and its series approximation, with practical examples demonstrating its effectiveness.
Contribution
The paper presents a novel evaluation formula for Wiener integrals that simplifies calculating the analytic Fourier-Feynman transform and its series approximation.
Findings
Evaluation formula effectively computes Wiener integrals.
Simplified calculation of the analytic Fourier-Feynman transform.
Series approximation method established for the transform.
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 very easily calculating 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.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · Advanced Mathematical Modeling in Engineering