Relationships involving generalized fourier–feynman transform, convolution and first variation

Huffman, Park and Skoug introduced a generalized Fourier–Feynman transform (GFFT) and a generalized convolution product (GCP) and they obtained the relationships between the GFFT and GCP for functionals in the Banach algebra 𝒮 introduced by Cameron and Storvick. In this paper, we investigate various relationships among the GFFT, GCP and generalized first variation for functionals in 𝒮.