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...
We study endpoint mapping properties of low-energy wave operators for Schr\"odinger operators $H=-\Delta+V$ on $\mathbb R^n$, $n\ge3$. In dimension four, we prove that a zero-energy resonance prevents $L^1$ boundedness, whether or not zero is also an eigenvalue, under $|V(x)|\lesssim\langle x\rangle^{-\beta}$ with $\be...
Han Cheng, Chang-Xing Miao, Xiao-Hua Yao· 0 citations
We establish sharp endpoint mapping properties for the wave operators $W_\pm(H,-\Delta)$ of two-dimensional Schr\"odinger operators $H=-\Delta+V$ with real-valued decaying potentials $V$. Together with the known non-endpoint $L^p$ theory, our results give a complete classification of the $L^p$ mapping properties of the...
Han Cheng, Chang-Xing Miao, Xiao-Hua Yao· 1 citation
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