A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II

We show that for certain bounded cylinder functions of the form F ( x ) = μ ˆ ( ( h 1 , x ) ∼ , ... , ( h n , x ) ∼ ) , x ∈ B where μ ˆ : ℝ n → ℂ is the Fourier-transform of the complex-valued Borel measure μ on ℬ ( ℝ n ) , the Borel σ -algebra of ℝ n with ‖ μ ‖ < ∞ , the analytic Feynman integral of F 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 functions F ( x ) = f ( ( h 1 , x ) ∼ , ... , ( h n , x ) ∼ ) , x ∈ B . We prove a change of scale formula for Wiener integrals of F on the abstract Wiener space.