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

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Abstract

We prove that the dimension of the space of energy finite bounded solutions of the Schrödinger operator is invariant under rough isometries between graphs of bounded degree. This result generalizes those of Soardi and of the present author.

Original languageEnglish
Pages (from-to)167-177
Number of pages11
JournalDiscrete Mathematics
Volume263
Issue number1-3
DOIs
StatePublished - 28 Feb 2003

Bibliographical note

Funding Information:
E-mail address: yonghah@ewha.ac.kr (Y.H. Lee). 1This work was supported by Korea Research Foundation Grant (KRF-2001-003-D00008).

Keywords

  • Almost every path
  • Extremal length
  • Rough isometry

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