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We study the conditional integral transforms and conditional convolutions of functionals defined on $K[0, T]$. We consider a general vector-valued conditioning functions $X_k (x) = \left(\gamma_1 (x), \ldots, \gamma_k (x)\right)$ where $\gamma_j (x)$ are Gaussian random variables on the Wiener space which need not depend upon the values of $x$ at only finitely many points in $(0, T]$. We then obtain several relationships and formulas for the conditioning functions that exist among conditional integral transform, conditional convolution and first variation of functionals in $E_\sigma$.
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참고문헌 (14)
참고문헌 신청
R.H.Cameron / 1951 / The first variation of an indefinite Wiener integral / Proc. Amer. Math. Soc 2
R.H.Cameron / 1945 / Fourier-Wiener transforms of analytic functionals / Duke Math. J 12:489~507
R.H.Cameron / 1976 / An L2 analytic Fourier-Feynman transform / Michigan Math. J 23:1~30
D.M.Chung / 1989 / Conditional analytic Feynman integrals and a related Schrodinger integral equation / Siam. J. Math. Anal 20:950~965
B.A.Fuks / 1963 / Theory of analytic functions of several complex variables / Amer. Math. Soc
R.H.Cameron / 1945 / Fourier-Wiener transforms of analytic functionals / Duke Math. J 12:489~507
R.H.Cameron / 1976 / An L2 analytic Fourier-Feynman transform / Michigan Math. J 23:1~30
D.M.Chung / 1989 / Conditional analytic Feynman integrals and a related Schrodinger integral equation / Siam. J. Math. Anal 20:950~965
B.A.Fuks / 1963 / Theory of analytic functions of several complex variables / Amer. Math. Soc
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