Bulletin of the
Korean Mathematical Society BKMS

Let $M$ be a complete Riemannian manifold and ${\mathcal L}$ be a Schr\"o\-d\-inger operator on $M$. We prove that if $M$ has finitely many $\mathcal L$-nonpara\-bol\-ic ends, then the space of bounded $\mathcal L$-harmonic functions on $M$ has the same dimension as the sum of dimensions of the spaces of bounded $\mathcal L$-harmonic functions on each $\mathcal L$-nonparabolic end, which vanish at the boundary of the end.

Keywords: Schrodinger operator, $\mathcal L$-harmonic function, $\mathcal L$-massive set, end

MSC numbers: 58J05, 35J10