On a continuum limit of discrete Schrodinger operators on square lattices

The norm resolvent convergence of discrete Schrodinger operators to a continuum Schrodinger 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. Mathematics Subject Cla...

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Bibliographic Details
Published inJournal of spectral theory Vol. 11; no. 1; p. 355
Main Authors Nakamura, Shu, Tadano, Yukihide
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2021
Subjects
Convergence (Mathematics)
Lattice theory
Mathematical research
Schrodinger equation
Japan
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ISSN1664-039X
DOI10.4171/JST/343

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Summary:The norm resolvent convergence of discrete Schrodinger operators to a continuum Schrodinger 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. Mathematics Subject Classification (2010). Primary: 47A10; Secondary: 47B39,47A25, 81U05. Keywords. Discrete Schrodinger operators, continuum limit, convergence of the spectrum.
ISSN:1664-039X
DOI:10.4171/JST/343