FEYNMAN FORMULAS FOR EVOLUTION EQUATIONSWITH LEVY LAPLACIANS ON MANIFOLDS

摘要

A Feynman formula is a representation of a solution of Cauchy problem for an evolution partial differential (or pseudodifferential) equation by a limit of some Gaussian or complex Gaussian finite dimensional integrals when their multiplicity tends to infinity. Some Feynman formulas for solutions of heat and Schrodinger type equations with Levy Laplacians on the infinite dimensional manifold which is the set of mappings of a real segment into a Riemannian manifold are obtained.