A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II. (22nd January 2001) - Kim, Young Sik
Abstract : We show that for certain bounded cylinder functions of the formF ( x ) = μ ˆ ( ( h 1, x ) ∼, ..., ( h n, x ) ∼ ), x ∈ B whereμ ˆ : ℝ n → ℂ is the Fourier-transform of the complex-valued Borel measureμ onℬ ( ℝ n ), the Borelσ -algebra ofℝ n with‖ μ ‖ < ∞, the analytic Feynman integral ofF exists, although the analytic Feynman integral, lim z → − i q I a w ( F ; z ) = lim z → − i q ( z / 2 π ) n / 2 ∫ ℝ n f ( u → ) exp − ( z / 2 ) | u → | 2 d u →, do not always exist for bounded cylinder functionsF ( x ) = f ( ( h 1, x ) ∼, ..., ( h n, x ) ∼ ), x ∈ B . We prove a change of scale formula for Wiener integrals ofF on the abstract Wiener space.