# Generalized Fourier--Feynman transforms and generalized convolution products on Wiener space II

## TL;DR

This paper extends the fundamental relationship between generalized Fourier--Feynman transforms and convolution products from Euclidean spaces to Wiener space, an infinite-dimensional Banach space, enhancing the theoretical framework of stochastic analysis.

## Contribution

It introduces the second type fundamental relationship between these transforms and convolutions on Wiener space, generalizing classical Euclidean space results to infinite dimensions.

## Key findings

- Established the second type fundamental relationship on Wiener space.
- Extended classical Fourier-convolution structure to infinite-dimensional Banach spaces.
- Provided a theoretical foundation for future stochastic analysis applications.

## Abstract

The purpose of this article is to present the second type fundamental relationship between the generalized Fourier--Feynman transform and the generalized convolution product on Wiener space. The relationships in this article are also natural extensions (to the case on an infinite dimensional Banach space) of the structure which exists between the Fourier transform and the convolution of functions on Euclidean spaces.