JournalsjstVol. 11, No. 1pp. 355–367

On a continuum limit of discrete Schrödinger operators on square lattice

  • Shu Nakamura

    Gakushuin University, Tokyo, Japan

  • Yukihide Tadano

    Kyoto University and Tokyo University of Science, Japan
On a continuum limit of discrete Schrödinger operators on square lattice cover
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Abstract

The norm resolvent convergence of discrete Schrödinger operators to a continuum Schrödinger operator in the continuum limit is proved under relatively weak assumptions. This result implies, in particular, the convergence of the spectrum with respect to the Hausdorff distance.

Cite this article

Shu Nakamura, Yukihide Tadano, On a continuum limit of discrete Schrödinger operators on square lattice. J. Spectr. Theory 11 (2021), no. 1, pp. 355–367

DOI 10.4171/JST/343