(1) Department of Mathematics, Yonsei University, Seoul, 120-749, Korea;(2) Department of Mathematics, Yonsei University, Wonju, 220-710, Korea
Abstract:
In this paper, we introduce a simple formula for conditional Wiener integrals over , 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 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 formwhich are of interest in Feynman integration theories and quantum mechanics.