Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2023; 60(5): 1221-1235

Online first article July 19, 2023      Printed September 30, 2023

https://doi.org/10.4134/BKMS.b220602

Copyright © The Korean Mathematical Society.

Conditional Fourier--Feynman transform and conditional convolution product associated with infinite dimensional conditioning function

Jae Gil Choi, Sang Kil Shim

Dankook University; Dankook University

Abstract

In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier--Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

Keywords: Wiener space, conditional Fourier--Feynman transform, conditional convolution product, Paley--Wiener--Zygmund stochastic integral

MSC numbers: Primary 28C20, 46G12; Secondary 60J65