- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Bounded solutions for the Schrodinger operator on Riemannian manifolds Bull. Korean Math. Soc. 2007 Vol. 44, No. 3, 507-516 Printed September 1, 2007 Seok Woo Kim and Yong Hah Lee Konkuk University, Ewha Womans University Abstract : 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 Downloads: Full-text PDF