Relationships between Fourier-Feynman transforms and Wiener integrals on abstract Wiener spaces. (English) Zbl 1020.28009
Summary: The purpose of this paper is to establish relationships between \(L_p\)-analytic Fourier-Feynman transforms and Wiener integrals of certain cylinder functions of the form
\[
F(x)= f((h_1, x)^\sim,\dots, (h_n,x)^\sim)
\]
for scale-a.e. \(x\in B\), where \(f\in L_p(\mathbb{R}^n)\) and \(1\leq p\leq 2\), on abstract Wiener spaces.
MSC:
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 46G12 | Measures and integration on abstract linear spaces |
| 81S40 | Path integrals in quantum mechanics |
Keywords:
abstract Wiener space; Fourier-Feynman transform; change of scale formula; Wiener integrals; cylinder functionsReferences:
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