Sequential Generalized Transforms on Function Space

Abstract

We define two sequential transforms on a function space $C_{\mathrm{a,b}}[\mathrm{0},T]$ induced by generalized Brownian motion process. We then establish the existence of the sequential transforms for functionals in a Banach algebra of functionals on $C_{\mathrm{a,b}}[\mathrm{0},T]$. We also establish that any one of these transforms acts like an inverse transform of the other transform. Finally, we give some remarks about certain relations between our sequential transforms and other well-known transforms on $C_{\mathrm{a,b}}[\mathrm{0},T]$.