The Feynman maps and the Wiener integral

By introducing the family of Feymnan maps J^s, we show that our earlier definition of the Feynman path integral J = J¹ can be obtained as the analytic continuation of the Wiener integral E = J^-i. This leads to some new results for the Wiener and Feynman integrals. We establish a translation and Cameron-Martin formula for the Feynman maps J ^s, having applications to nonrelativistic quantum mechanics. We also estalish a (weak) dominated convergence theorem for J¹ = J. © 1978 American Institute of Physics.