Conditional Fourier-Feynman transform and conditional convolution product associated with vector-valued conditioning function

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2023, v.30 no.2, pp.155-167

https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.155

Ae Young Ko (Basic Science and Mathematics Center, Dankook University)
Jae Gil Choi (School of General Education, Dankook University)

Ae Young Ko, & Jae Gil Choi. (2023). CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH VECTOR-VALUED CONDITIONING FUNCTION. 한국수학교육학회지시리즈B:순수및응용수학, 30(2), 155-167, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.155

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Abstract

In this paper, we use a vector-valued 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 functionals 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

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논문 상세

Vol.30 No.2

CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH VECTOR-VALUED CONDITIONING FUNCTION

Conditional Fourier-Feynman transform and conditional convolution product associated with vector-valued conditioning function

Abstract

한국수학교육학회지시리즈B:순수및응용수학