EXISTENCE THEOREMS AND EVALUATION FORMULAS FOR SEQUENTIAL YEH-FEYNMAN INTEGRALS

We establish the existence of the sequential Yeh-Feynman integral for functionals of the form F (x) = G(x)Ψ(x(S, T )), where G belongs to a Banach algebra of sequential Yeh-Feynman integrable functionals and Ψ need not be bounded or continuous. We also give formulas evaluating the integrals of these functionals. Note that these functionals are often employed in the application of the Feynman integral to quantum theory, and Ψ corresponds to the initial condition associated with Schrödinger equation.