A change of scale formula for a function space integral on 𝐶_{𝑎,𝑏}[0,𝑇]

Yoo, Il; Kim, Bong; Kim, Byoung

doi:10.1090/S0002-9939-2013-11598-4

A change of scale formula for a function space integral on $C_{a,b}[0,T]$
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Proc. Amer. Math. Soc. 141 (2013), 2729-2739 Request permission

Abstract:

Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in a Banach algebra ${\mathcal S}$ on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class ${\mathcal F}(B)$ and in a generalized Fresnel class ${\mathcal F}_{A_1,A_2}$ on abstract Wiener space. We establish a relationship between a function space integral and a generalized analytic Feynman integral on $C_{a,b}[0,T]$ for functionals in a Banach algebra ${\mathcal S}(L_{a,b}^2[0,T])$. Moreover, we obtain a change of scale formula for a function space integral on $C_{a,b}[0,T]$ of these functionals.

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