TY - JOUR
T1 - Fourier-Feynman transform, convolution and first variation of functionals on abstract Wiener space
AU - Chang, K. S.
AU - Kim, B. S.
AU - Yoo, I.
PY - 2000
Y1 - 2000
N2 - Park, Skoug and Storvick examined various relationships among the first variation, the Fourier-Feynman transform, and the convolution product for functional, on classical Wiener space (C0[0, 1], m), which belong to some Banach algebra S. In this paper, we extend the above concepts to an abstract Wiener space (B, v) and establish various relationships involving the concepts of Fourier-Feynman transform, convolution, and the first variation for functionals in the Fresnel class F(B) which corresponds to S. Since the Fresnel class F(B) is the abstract Wiener space setting of the Banach algebra S, our results include the above results as special cases.
AB - Park, Skoug and Storvick examined various relationships among the first variation, the Fourier-Feynman transform, and the convolution product for functional, on classical Wiener space (C0[0, 1], m), which belong to some Banach algebra S. In this paper, we extend the above concepts to an abstract Wiener space (B, v) and establish various relationships involving the concepts of Fourier-Feynman transform, convolution, and the first variation for functionals in the Fresnel class F(B) which corresponds to S. Since the Fresnel class F(B) is the abstract Wiener space setting of the Banach algebra S, our results include the above results as special cases.
KW - Abstract Wiener space
KW - Analytic Feynman integral
KW - Convolution
KW - Fourier-Feynman transform
KW - The first variation
UR - http://www.scopus.com/inward/record.url?scp=0037711858&partnerID=8YFLogxK
U2 - 10.1080/10652460008819285
DO - 10.1080/10652460008819285
M3 - Article
AN - SCOPUS:0037711858
SN - 1065-2469
VL - 10
SP - 179
EP - 200
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
IS - 3-4
ER -