期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2001
卷号：25
DOI：10.1155/S0161171201004537
出版社：Hindawi Publishing Corporation
摘要：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.
