Relationships between generalized Wiener integrals and conditional analytic Feynman integrals over continuous paths

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t], and define a random vector Z_n: C[0, t] → Rⁿ⁺¹ by Zn(x)=(x(0)+a(0),∫ot1h(s)dx(s)+x(0)+a(t1),..,∫0tnh(s)dx(s)+x(0)+a(tn)), where a ∈ C[0, t], h ∈ L₂[0, t], and 0 < t₁ <.. < t_n ≤ t is a partition of [0, t]. Using simple formulas for generalized conditional Wiener integrals, given Z_n we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions F in a Banach algebra which corresponds to Cameron-Storvick’s Banach algebra S. Finally, we express the generalized analytic conditional Feynman integral of F as a limit of the non-conditional generalized Wiener integral of a polygonal function using a change of scale transformation for which a normal density is the kernel. This result extends the existing change of scale formulas on the classical Wiener space, abstract Wiener space and the analogue of the Wiener space C[0, t].