Si-Si Huang

Resolvent Expansions at All Spectral Thresholds for Three-Dimensional Discrete Schr\"odinger Operators

This paper studies resolvent expansions at all four spectral thresholds for the discrete Schr\"odinger operator $H=-\Delta+V $ on $\Z^3$, where $\Delta$ denotes the discrete Laplacian on $\mathbb{Z}^3$ and $V(n)$ is a real-valued decaying potential of $\mathbb{Z}^3$. At the thresholds 0, 4, 8, and 12, we first give a c...