Generalized Integral Transforms via the Series Expressions

Abstract

From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods.

A matrix transform on function space with related topics

“…Furthermore, v, x is a Gaussian random variable with mean 0 and variance v 2 2 . For a more detailed study of the PWZ stochastic integral, see [1,5,7,9,14,15,18].…”

Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function

“…In [11]- [13], Cameron and Martin expanded the theory about the translation and transformation theory for the Wiener integral. In [14], Chung expanded the generalized integral transforms for Wiener integrals. In [15], Gaysinsky and Goldstein expanded the self-adjointness of Schrodinger operator and Wiener integrals.…”