Abstract
The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space C0[0,T], where θ(t,u) is a Fourier-Stieltjes transform of a complex Borel measure.
Highlights
The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral
Storvick, proved relationships between Wiener integrals and analytic Feynman integrals to prove a change of scale formula for Wiener integrals (1987)
We investigate the interesting behavior of the scale factor for the Wiener integral by analyzing the analytic Wiener integral as followings: For real ρ > 0
Summary
H. Cameron wrote the paper about the translation pathology of a Wiener space (1954). T. Martin proved some theorems on the transformation and the translation and used the expression of the change of scale for Wiener integrals (1944-1947). A. Storvick, proved relationships between Wiener integrals and analytic Feynman integrals to prove a change of scale formula for Wiener integrals (1987). S. Kim proved relationships between Wiener integrals and analytic Feynman integrals and proved a change of scale formula for Wiener integrals about cylinder functions on the abstract Wiener space (1998-2001). In [13] [14] [15] [16], Kim proved relationships among the Fourier transform and the Fourier Feynman transform and the convolution on the abstract Wiener space (2006-2016). We will find a very interesting behavior of a scale factor ρ > 0 for the Wiener integral
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