Conditional generalized Fourier--Feynman transforms on function space and an application
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In this paper, we study generalized Fourier--Feynman transform(GFFT)s and conditional generalized Fourier--Feynman transform\break(CGFFT)s for functionals on the function space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ is the space of continuous sample paths of the generalized Brownian motion process(GBMP) determined by continuous functions $a$ and $b$ defined on the time interval $[0,T]$. The aim of this paper is to provide representations of inverse forms of the GFFTs. To do this work, we first provide inverse forms of the CGFFTs of exponential type functionals on $C_{a,b}[0,T]$. Using these, we finally formulate inverse forms of the GFFTs.
Abstract
In this paper, we study generalized Fourier--Feynman transform(GFFT)s and conditional generalized Fourier--Feynman transform\break(CGFFT)s for functionals on the function space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ is the space of continuous sample paths of the generalized Brownian motion process(GBMP) determined by continuous functions $a$ and $b$ defined on the time interval $[0,T]$. The aim of this paper is to provide representations of inverse forms of the GFFTs. To do this work, we first provide inverse forms of the CGFFTs of exponential type functionals on $C_{a,b}[0,T]$. Using these, we finally formulate inverse forms of the GFFTs.