Generalized convolution product for an integral transform on a Wiener space

Authors

BYOUNG SOO KIM
IL YOO

DOI

10.3906/mat-1601-79

Abstract

We introduce a generalized convolution product $(F*G)_{\vec\alpha,\vec\beta}$ for integral transform ${\mathcal F}_{\gamma,\eta}$ for functionals defined on $K[0,T]$, the space of complex valued continuous functions on $[0,T]$ that vanish at zero. We study some interesting properties of our generalized convolution product and establish various relationships that exist among the generalized convolution product, the integral transform, and the first variation for functionals defined on $K[0,T]$. We also discuss the associativity of the generalized convolution product.

Keywords

Wiener integral, integral transform, generalized convolution product, first variation

First Page

940

Last Page

955

Recommended Citation

KIM, BYOUNG SOO and YOO, IL (2017) "Generalized convolution product for an integral transform on a Wiener space," Turkish Journal of Mathematics: Vol. 41: No. 4, Article 14. https://doi.org/10.3906/mat-1601-79
Available at: https://journals.tubitak.gov.tr/math/vol41/iss4/14