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In this paper, we define conditional integrals on abstract Wiener and Hilbert spaces and then obtain a formula for evaluating the integrals. We use this formula to establish the existence of conditional Feynman integrals for the classes Λq(B) and Λq(H) of functions on abstract Wiener and Hilbert spaces and then specialize this result to provide the fundamental solution to the Schr¨odinger equation with the forced harmonic oscillator.
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