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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.30 No.2

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Jae Gil Choi
Ae, Y. K. , & Jae, G. C. (2023). Conditional Fourier-Feynman transform and conditional convolution product associated with vector-valued conditioning function. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 30(2), 155-167, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.155

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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