Analytic operator-valued Feynman integrals of certain finite-dimensional functionals on function space

Abstract

In this paper we establish the existence of an operator $J_q^\mathrm{an}(F)$ for appropriate functionals of the form

$$\begin{aligned} F(x)=f(\langle {\theta _1,x}\rangle ,\ldots ,\langle {\theta _n,x}\rangle ) \end{aligned}$$

where $\langle {\theta _j,x}\rangle$ denotes the Paley–Wiener–Zygmund stochastic integral with $x$ in $C_{a,b}[0,T]$ and $\{\theta _1,\ldots ,\theta _n\}$ is an orthonormal set of functions in $L_{a,b}^2[0,T]$