Ergodic-Type Limit Theorem for Fundamental Solutions of Critical Schrodinger Operators

摘要

Let {Xt}t0 be the symmetric -stable process with generator H=(-)/2 for 02. For a positive Radon measure , we define the Schrodinger operator H=H- and consider the fundamental solution of the equation u/t=-Hu. If is critical, the behavior of the fundamental solution is different from that of the transition density function of {Xt}t0. In this paper, we give a certain ergodic-type limit theorem for fundamental solutions of critical Schrodinger operators.