TY - JOUR
T1 - Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space
AU - Chang, K. S.
AU - Kim, B. S.
AU - Song, T. S.
AU - Yoo, I.
PY - 2002/8
Y1 - 2002/8
N2 - In this paper, we define an Lp analytic Fourier-Feynman transform on C0(B), the space of abstract Wiener space valued continuous functions on [0, T]. We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C0(B) having the form F(x) =f((h1, x(s1))̃, ..., (hm, x(Sn))̃). Moreover we present various relationships involving convolution and the transforms.
AB - In this paper, we define an Lp analytic Fourier-Feynman transform on C0(B), the space of abstract Wiener space valued continuous functions on [0, T]. We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C0(B) having the form F(x) =f((h1, x(s1))̃, ..., (hm, x(Sn))̃). Moreover we present various relationships involving convolution and the transforms.
KW - Abstract Wiener space
KW - Analytic Feynman integral
KW - Convolution
KW - Fourier-Feynman transform
UR - http://www.scopus.com/inward/record.url?scp=0036023571&partnerID=8YFLogxK
U2 - 10.1080/10652460213523
DO - 10.1080/10652460213523
M3 - Article
AN - SCOPUS:0036023571
SN - 1065-2469
VL - 13
SP - 345
EP - 362
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
IS - 4
ER -