ROUGH ISOMETRY AND THE SPACE OF BOUNDED ENERGY FINITE SOLUTIONS OF THE SCHRODINGER OPERATOR ON GRAPHS

Title & Authors
ROUGH ISOMETRY AND THE SPACE OF BOUNDED ENERGY FINITE SOLUTIONS OF THE SCHRODINGER OPERATOR ON GRAPHS
Kim, Seok-Woo; Lee, Yong-Hah; Yoon, Joung-Hahn;

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 Schr$\small{\ddot{o}}$dinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3].
Keywords
infinite graph;$\small{Schr\ddot{o}dinger}$ operator;bounded energy finite solution;rough isometry;
Language
English
Cited by
References
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