Uniform bounds of discrete Birman–Schwinger operators
Copyright policy )Uniform bounds of discrete Birman–Schwinger operators
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.
20pages, no figures
- University of Tokyo Japan
discrete Schrödinger operators, FOS: Physical sciences, Mathematical Physics (math-ph), A priori estimates in context of PDEs, resolvents, Mathematics - Analysis of PDEs, Schrödinger operator, Schrödinger equation, FOS: Mathematics, 47A10, 47A40, Discrete version of topics in analysis, limiting absorption principle, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis, Analysis of PDEs (math.AP)
discrete Schrödinger operators, FOS: Physical sciences, Mathematical Physics (math-ph), A priori estimates in context of PDEs, resolvents, Mathematics - Analysis of PDEs, Schrödinger operator, Schrödinger equation, FOS: Mathematics, 47A10, 47A40, Discrete version of topics in analysis, limiting absorption principle, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis, Analysis of PDEs (math.AP)
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