On a continuum limit of discrete Schrödinger operators on square lattice

Published 26 Mar 2019 in math-ph, math.FA, math.MP, and math.SP | (1903.10656v1)

Abstract: The norm resolvent convergence of discrete Schr\"odinger operators to a continuum Schr\"odinger 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.

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