Discrete inverse problems for the Schrödinger operator on the multi-dimensional square lattice with partial Cauchy data. (7th April 2016)

• Record Type: Journal Article
• Authors: Horváth, Miklós; Markó, Zoltán
• Is Part Of: Inverse problems. Volume 32:Number 5(2016:May)
• Publication Date: 2016-04-07
• Subjects: discrete Schödinger operator -- Dirichlet-to-Neumann map -- partial Cauchy data -- potential reconstruction; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/5/055006
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Motivated by the known results for an ongoing problem, in this paper we define the partial Cauchy data set for the discrete Schrödinger operator on a finite subset of the grid, and we prove a reconstruction theorem for the potential. Our methods are applicable in some general situations; we give a potential reconstruction theorem in the case of the hexagonal lattice as an example.