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Jacob Schach Møller

The discrete Laplacian: A Bessel function approach

Abstract:We discuss how to use optimal estimates on Bessel functions by Krasikov and Landau to derive L^p-weighted estimates for the free propagator and resolvent of the discrete Laplacian on a cubic lattice. As an application, we shall discuss an associated Birman-Schwinger equation and derive consequences for the spectral and scattering theory for discrete Schrödinger operators.

The talk is based on joint work with Evgeny Korotyaev.