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http://dx.doi.org/10.4134/BKMS.2011.48.2.223

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

Chang, Seung-Jun (Department of Mathematics Dankook University)
Lee, Il-Yong (Department of Mathematics Dankook University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 223-245 More about this Journal
Abstract
In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.
Keywords
generalized Brownian motion process; generalized analytic Feynman integral; generalized analytic Fourier-Feynman transform; convolution product; Fresnel type class;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
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