Uniform bounds of discrete Birman-Schwinger operators

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 non-uniformly 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.

arXiv comment20pages, no figures

References in corpus (4)

• Eigenvalue bounds for Schrödinger operators with complex potentials
• Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations
• Weighted estimates for the discrete Laplacian on the cubic lattice
• Bounds on the Pure Point Spectrum of Lattice Schrödinger Operators