6c

The Discrete Laplacian: A Bessel Function Aproach

Jacob Schach Moller 氏
Aarhus University, Denmark



アブストラクト:
The talk is based on joint work with Evgeny Korotyaev.
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 point spectrum and singular continuous spectrum of discrete Schrodinger operators.