A SOLUTION TO SCHRODINGERS PROBLEM OF NONLINEAR INTEGRAL-EQUATIONS

A solution of Schrodinger's system of non-linear integral equations de termines the rate function of a large deviation principle for kernels with prescribed marginal distributions. This kind of large deviation p rinciple has some meaning in quantum mechanics. Diffusion equations as sociated with Schrodinger equations have typically transition function s with singular creation and killing. Hence they provide measurable no n-negative generally unbounded kernels which may vanish on sets with p ositive measure and which can possess infinite mass. For Schrodinger s ystems with such kernels, a solution is proved to exist uniquely in te rms of a product measure. It is obtained from a variational principle for the local adjoint of a product measure endomorphism. The generally unbounded factors of the solution are characterized by integrability properties.