A Change of Scale Formula for Wiener Integrals of Cylinder Functions on the Abstract Wiener Space Ii
نویسنده
چکیده
We show that for certain bounded cylinder functions of the form F(x) = μ̂((h1,x)∼, . . . ,(hn,x)∼), x ∈ B, where μ̂ :Rn → C is the Fourier-transform of the complexvalued Borel measure μ on (Rn), the Borel σ -algebra of Rn with ‖μ‖ < ∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iq Iaw(F ;z)= limz→−iq(z/2π) ∫ Rn f( →u)exp{−(z/2)| →u|2}d →u, 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. 2000 Mathematics Subject Classification. Primary 28C20.
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