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Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 161-180
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In this paper, we introduce a simple formula for conditional Wiener integrals over $C_0(\mathbb{B})$, the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on $C_0(\mathbb{B})$ in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral for functionals of the form \[ \exp \biggl \lbrace \int _0^T \theta (s, x(s))\mathrm{d}\eta (s) \biggr \rbrace \] which are of interest in Feynman integration theories and quantum mechanics.
In this paper, we introduce a simple formula for conditional Wiener integrals over $C_0(\mathbb{B})$, the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on $C_0(\mathbb{B})$ in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral for functionals of the form \[ \exp \biggl \lbrace \int _0^T \theta (s, x(s))\mathrm{d}\eta (s) \biggr \rbrace \] which are of interest in Feynman integration theories and quantum mechanics.
Classification : 28C20, 46G12, 81S40
Keywords: Banach algebra $S_{\mathbb{B}}^{\prime \prime }$; Banach space $S_{n, \mathbb{B}}^{\prime \prime }$; conditional Wiener integral; conditional Feynman integral; simple formula for conditional Wiener integrals 
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     title = {Evaluation formulas for a conditional {Feynman} integral over {Wiener} paths in abstract {Wiener} space},
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}
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Chang, Kun Soo; Cho, Dong Hyun; Yoo, Il. Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 161-180. http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a13/

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