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In this paper,
for functionals of a generalized Brownian motion process,
we show that the generalized Fourier-Feynman transform
of the convolution product
is a product of multiple transforms
and that the conditional generalized Fourier-Feynman transform
of the conditional convolution product
is a product of multiple conditional transforms.
This allows us to compute the (conditional) transform
of the (conditional) convolution product
without computing the (conditional) convolution product.
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참고문헌 (17)
참고문헌 신청
C. Park / 1988 / A simple formula for conditional Wiener integrals with applications / Pacific J. Math. 135 : 381 ~ 394
C. Park / 2001 / Conditional Fourier-Feynman transforms and conditional convolution products / J. Korean Math. Soc. 38 : 61 ~ 76
G. W. Johnson / 1979 / An Lp analytic Fourier-Feynman transform / Michigan Math. J. 26 : 103 ~ 127
H.-H. Kuo / 1975 / Gaussian Measures in Banach Spaces, Lecture Notes in Math. / Springer
J. Yeh / 1971 / Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increment / Illinois J. Math. 15 : 37 ~ 46
C. Park / 2001 / Conditional Fourier-Feynman transforms and conditional convolution products / J. Korean Math. Soc. 38 : 61 ~ 76
G. W. Johnson / 1979 / An Lp analytic Fourier-Feynman transform / Michigan Math. J. 26 : 103 ~ 127
H.-H. Kuo / 1975 / Gaussian Measures in Banach Spaces, Lecture Notes in Math. / Springer
J. Yeh / 1971 / Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increment / Illinois J. Math. 15 : 37 ~ 46
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