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

摘要

We show that for certain bounded cylinder functions of the formF(x)=μˆ((h1,x)∼,...,(hn,x)∼),x∈Bwhereμˆ:ℝn→ℂisthe Fourier-transform of the complex-valued Borel measureμonℬ(ℝn), the Borelσ-algebra ofℝnwith‖μ‖<∞, the analytic Feynmanintegral ofFexists, although the analytic Feynman integral,limz→−iqIaw(F;z)=limz→−iq(z/2π)n/2∫ℝnf(u→)exp{−(z/2)|u→|2}du→, do notalways exist for bounded cylinder functionsF(x)=f((h1,x)∼,...,(hn,x)∼),x∈B. We prove a change of scale formula for Wiener integrals ofFonthe abstract Wiener space.