International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 4, Pages 231-237

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

Young Sik Kim

BK-21 Mathematical Science Division, Department of Mathematics, Seoul National University, Seoul 151-742, South Korea

Received 24 January 2000

Copyright © 2001 Young Sik Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We show that for certain bounded cylinder functions of the form F(x)=μˆ((h1,x),...,(hn,x)), xB where μˆ:n is the Fourier-transform of the complex-valued Borel measure μ on (n), the Borel σ-algebra of n with μ<, the analytic Feynman integral of F exists, although the analytic Feynman integral, limziqIaw(F;z)=limziq(z/2π)n/2nf(u)exp{(z/2)|u|2}du, do not always exist for bounded cylinder functions F(x)=f((h1,x),...,(hn,x)), xB. We prove a change of scale formula for Wiener integrals of F on the abstract Wiener space.