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 A1,A2 than the Fresnel class (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 , where G∈ (B)and Ψ = ψ + ϕ with ψ ∈ L 1(ℝn) and ϕ is the Fourier transform of a complex Borel measure of bounded variation on ℝn. We also prove a translation theorem for the analytic Feynman integral of the above functionals.
@article{bwmeta1.element.doi-10_2478_s11533-010-0019-2,
author = {Byoung Kim and Il Yoo and Dong Cho},
title = {Fourier-Feynman transforms of unbounded functionals on abstract Wiener space},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {616-632},
zbl = {1204.28022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0019-2}
}
Byoung Kim; Il Yoo; Dong Cho. Fourier-Feynman transforms of unbounded functionals on abstract Wiener space. Open Mathematics, Tome 8 (2010) pp. 616-632. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0019-2/
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