Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
qr-code QR
Code

Article

HOME ALL ARTICLES View

Commun. Korean Math. Soc. 2010; 25(4): 609-614

Printed December 1, 2010

https://doi.org/10.4134/CKMS.2010.25.4.609

Copyright © The Korean Mathematical Society.

Rough isometry and the space of bounded energy finite solutions of the Schr\odinger operator on graphs

Seok Woo Kim, Yong Hah Lee, and Joung-Hahn Yoon

Konkuk University, Ewha Womans University, Donga University

Abstract

Go to

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

Article Tools

Stats or Metrics

Share this article on :

Related articles in CKMS

more +