A generalized analytic Fourier-Feynman transform on the product function space $C_{a,b}^2[0,T]$ and related topics

TL;DR

This paper develops a generalized Fourier-Feynman transform for functionals on a product space of continuous functions, exploring its properties and variations within a Fresnel type class.

Contribution

It introduces a new generalized analytic Fourier-Feynman transform on the product function space and studies its first variation, extending existing theories.

Findings

Established properties of the generalized Fourier-Feynman transform.

Derived results on the first variation of functionals in the Fresnel type class.

Extended the theory to the product space setting.

Abstract

In this paper we obtain various results involving the generalized analytic Fourier-Feynman transform and the first variation of functionals in a Fresnel type class defined on the product function space $C_{a,b}^2[0,T]$.