Inverse boundary value problems for discrete Schrödinger operators on the multi-dimensional square lattice

Hisashi Morioka

doi:10.3934/ipi.2011.5.715

Article Contents

2011, Volume 5, Issue 3: 715-730. Doi: 10.3934/ipi.2011.5.715

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Inverse boundary value problems for discrete Schrödinger operators on the multi-dimensional square lattice

Hisashi Morioka^1,

1.
Graduate school of pure and applied sciences, University of Tsukuba, Tennnoudai 1-1-1, Tsukuba, Ibaraki, 305-0821

Received: July 31, 2010

Revised: April 30, 2011

Published: July 2011

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Abstract

We consider an inverse boundary value problem for a discrete Schrödinger operator $-\Delta + \hat{q} $ on a bounded domain in the square lattice. We define an analogue of the Dirichlet-to-Neumann map, and give a reconstruction procedure of the potential $\hat{q} $ from the D-to-N map for all energies.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 39A12.

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