Homogenization of the two-dimensional periodic Dirac operator

Abstract

We consider the homogenization problem for the two-dimensional periodic Dirac operator with magnetic potential of two types: singular and nonsingular. Based on the operator-theoretic approach due to M. Birman and T. Suslina, we approximate the resolvent in the space of bounded operators acting in $ {L_2}\left( {{{\mathbb{R}}^2};{{\mathbb{C}}^2}} \right) $ with order-sharp error estimates. Bibliography: 4 titles.