Series expansions of the transform with respect to the Gaussian process

Abstract

In this paper, we consider the Fourier-type functionals introduced in [Chung HS, Tuan VK. Fourier-type functionals on Wiener space. Bull Korean Math Soc. 2012;49:609–619] and used in [Lee IY, Chung HS, Chang SJ. Series expansions of the analytic Feynman integral for the Fourier-type functional. J Korean Soc Math Educ Ser B. 2012;19:87–102]. We first establish the existence of the transform with respect to the Gaussian process for the Fourier-type functionals. We then obtain the various relationships for the transform with respect to the Gaussian process of the Fourier-type functionals which involved the ⋄-product and in addition, establish various integration formulas.