A Rellich type theorem for discrete Schrödinger operators

Hiroshi Isozaki; Hisashi Morioka

doi:10.3934/ipi.2014.8.475

Article Contents

2014, Volume 8, Issue 2: 475-489. Doi: 10.3934/ipi.2014.8.475

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A Rellich type theorem for discrete Schrödinger operators

Hiroshi Isozaki^1, and
Hisashi Morioka^1,

1.
Division of Mathematics, University of Tsukuba, Tennoudai 1-1-1, Tsukuba, Ibaraki, 305-8571

Received: June 30, 2013

Revised: October 31, 2013

Published: April 2014

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Abstract

An analogue of Rellich's theorem is proved for discrete Laplacians on square lattices, and applied to show unique continuation properties on certain domains as well as non-existence of embedded eigenvalues for discrete Schrödinger operators.

Keywords:

Mathematics Subject Classification: Primary: 47A40; Secondary: 81U40.

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References

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