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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (School of General Education, Dankook University)

Choi, Jae Gil. (2021). A REPRESENTATION FOR AN INVERSE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE. 한국수학교육학회지시리즈B:순수및응용수학, 28(4), 281-296, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.281

복사

Abstract

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space Ca,b[0, T]. The function space Ca,b[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 Ƶk of exponential-type functionals. We then establish that a composition of the Ƶk-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

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논문 상세

Vol.28 No.4

A REPRESENTATION FOR AN INVERSE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학