Bulletin of the
Korean Mathematical Society BKMS

In this paper, we define  a generalized integral transform $\mathcal{T}_\alpha$ on function space. We then establish some fundamental formulas for the integral transform $\mathcal{T}_\alpha$ involving the convolution product and the first variation. Furthermore, we establish some relationships among the integral transform, the convolution product and the first variation. Finally, we state an application with some examples.

Keywords: Integral transform, Wiener space, Fubini theorem, composition formula, Cameron-Storvick type theorem

MSC numbers: Primary 60J65; Secondary 28C20, 46B10