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

Yong Hah Lee

doi:10.1016/S0012-365X(02)00576-9

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

Yong Hah Lee

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English
Pages (from-to)	167-177
Number of pages	11
Journal	Discrete Mathematics
Volume	263
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(02)00576-9
State	Published - 28 Feb 2003

Keywords

Almost every path
Extremal length
Rough isometry

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10.1016/S0012-365X(02)00576-9

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title = "Rough isometry and energy finite solutions of the Schr{\"o}dinger operator on graphs",

abstract = "We prove that the dimension of the space of energy finite bounded solutions of the Schr{\"o}dinger operator is invariant under rough isometries between graphs of bounded degree. This result generalizes those of Soardi and of the present author.",

keywords = "Almost every path, Extremal length, Rough isometry",

author = "Lee, {Yong Hah}",

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).",

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N2 - 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.

AB - 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.

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KW - Extremal length

KW - Rough isometry

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DO - 10.1016/S0012-365X(02)00576-9

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VL - 263

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EP - 177

JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

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

Abstract

Keywords

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