Rough isometry and the space of bounded energy finite solutions of the Schrödinger operator on graphs

Abstract

We prove that if graphs of bounded degree are roughly isometric to each other, then the spaces of bounded energy finite solutions of the Schrödinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3]. © 2010 The Korean Mathematical Society.