Weighted estimates for the discrete Laplacian on the cubic lattice

2017/01/13 by Evgeny Korotyaev, Korotyaev, Evgeny L., Jacob Schach Møller +1 · 1 citation
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Physics Problems #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1701.03605

Abstract

We consider the discrete Laplacian Δ on the cubic lattice \mathbb Z^d, and deduce estimates on the group e^itΔ and the resolvent (Δ-z)^-1, weighted by ℓ^q(\mathbb Z^d)-weights for suitable q≥ 2. We apply the obtained results to discrete Schrödinger operators in dimension d≥ 3 with potentials from ℓ^p(\mathbb Z^d) with suitable p≥ 1.

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