GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS

Title & Authors
GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS
Chang, Seung-Jun; Lee, Il-Yong;

Abstract
In this paper, we de ne an $\small{L_p}$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\small{\cal{F}}$($\small{C_{a,b}}$[0, T]) which is called the Fresnel type class, and in more general class $\small{\cal{F}_{A_1;A_2}}$ of functionals de ned on general functio space $\small{C_{a,b}}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $\small{L_p}$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\small{\cal{F}}$($\small{C_{a,b}}$[0, T]) and in $\small{\cal{F}_{A_1,A_2}}$.
Keywords
generalized Brownian motion process;generalized analytic Feynman integral;generalized analytic Fourier-Feynman transform;convolution product;Fresnel type class;
Language
English
Cited by
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