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

ISSN : 1226-0657

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Vol.28 No.4

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A Representation for an Inverse Generalized Fourier-Feynman Transform associated with Gaussian Process on Function Space

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
2021, v.28 no.4, pp.281-296
https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.281
Choi, Jae Gil
Choi,, J. G. (2021). A Representation for an Inverse Generalized Fourier-Feynman Transform associated with Gaussian Process on Function Space. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 28(4), 281-296, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.281

Abstract

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C<sub>a,b</sub>[0, T]. The function space C<sub>a,b</sub>[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process &#x01B5;<sub>k</sub> of exponential-type functionals. We then establish that a composition of the &#x01B5;<sub>k</sub>-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

keywords
generalized Fourier-Feynman transform, generalized Brownian motion process, Gaussian process, exponential-type functional, inverse transform

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

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