International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 4, Pages 231-237
doi:10.1155/S0161171201004537

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

Abstract

We show that for certain bounded cylinder functions of the form F(x)=μˆ((h1,x)∼,...,(hn,x)∼), x∈B where μˆ:ℝn→ℂ is the Fourier-transform of the complex-valued Borel measure μ on ℬ(ℝn), the Borel σ-algebra of ℝn with ‖μ‖<∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iqIaw(F;z)=limz→−iq(z/2π)n/2∫ℝnf(u→)exp{−(z/2)|u→|2}du→, do not always exist for bounded cylinder functions F(x)=f((h1,x)∼,...,(hn,x)∼), x∈B. We prove a change of scale formula for Wiener integrals of F on the abstract Wiener space.