On a continuum limit of discrete Schrodinger operators on square lattices - Nakamura, Shu; Tadano, Yukihide (Journal of spectral theory, 2021)
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.