CHANGE OF SCALE FORMULAS FOR CONDITIONAL WIENER INTEGRALS AS INTEGRAL TRANSFORMS OVER WIENER PATHS IN ABSTRACT WIENER SPACE

In this paper, we derive a change of scale formula for conditional Wiener integrals, as integral transforms, of possibly unbounded functions over Wiener paths in abstract Wiener space. In fact, we derive the change of scale formula for the product of the functions in a Banach algebra which is equivalent to both the Fresnel class and the space of measures of bounded variation over a real separable Hilbert space, and the $L_p-type$ cylinder functions over Wiener paths in abstract Wiener space. As an application of the result, we obtain a change of scale formula for the conditional analytic Fourier-Feynman transform of the product of the functions.