Bounded solutions for the Schrodinger operator on Riemannian manifolds

Abstract

Let M be a complete Riemannian manifold and L be a Schrodinger operator on All. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded C-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on each L-nonparabolic end, which vanish at the boundary of the end.