Uniform bounds of discrete Birman–Schwinger operators

Tadano, Yukihide; Taira, Kouichi

doi:10.1090/tran/7882

Uniform bounds of discrete Birman–Schwinger operators
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by Yukihide Tadano and Kouichi Taira PDF

Trans. Amer. Math. Soc. 372 (2019), 5243-5262 Request permission

Abstract:

In this note, uniform bounds of the Birman–Schwinger operators in the discrete setting are studied. For uniformly decaying potentials, we obtain the same bound as in the continuous setting. However, for nonuniformly decaying potential, our results are weaker than in the continuous setting. As an application, we obtain unitary equivalence between the discrete Laplacian and the weakly coupled systems.

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