Rough isometry and the space of bounded energy finite solutions of the Schr\odinger operator on graphs
Commun. Korean Math. Soc. 2010 Vol. 25, No. 4, 609-614
https://doi.org/10.4134/CKMS.2010.25.4.609
Printed December 1, 2010
Seok Woo Kim, Yong Hah Lee, and Joung-Hahn Yoon
Konkuk University, Ewha Womans University, Donga University
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\"odinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi \cite{S1} and of Lee \cite{L}.
Keywords : infinite graph, Schr\odinger operator, bounded energy finite solution, rough isometry
MSC numbers : 31C20, 94C15
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