Fourier-Feynman transforms of unbounded functionals on abstract Wiener space |
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| Authors: | Byoung Soo Kim Il Yoo Dong Hyun Cho |
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| Affiliation: | (1) Department of Mathematics Education, Kon-Kuk University, Seoul, 143-701, Korea;(2) Department of Mathematics, Yonsei University, Seoul, 120-749, Korea;(3) Department of Mathematics, Yonsei University, Kangwondo, 220-710, Korea |
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| Abstract: | Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class $
mathcal{F}_{mathcal{A}_1 ,mathcal{A}_2 }
$
mathcal{F}_{mathcal{A}_1 ,mathcal{A}_2 }
A1,A2 than the Fresnel class $
mathcal{F}
$
mathcal{F}
(B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space having the form | $
Fleft( x right) = Gleft( x right)psi left( {left( {vec e,x} right)^ sim } right)
$
Fleft( x right) = Gleft( x right)psi left( {left( {vec e,x} right)^ sim } right)
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| Keywords: | |
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