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Spectral multipliers for Schr\"odinger operators.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zheng, Shijun |
| Copyright Year | 2020 |
| Abstract | We prove a sharp Hormander multiplier theorem for Schrodinger operators $H=-\Delta+V$ on $\mathbb{R}^n$. The result is obtained under certain condition on a weighted $L^\infty$ estimate, coupled with a weighted $L^2$ estimate for $H$, which is a weaker condition than that for nonnegative operators via the heat kernel approach. Our approach is elaborated in one dimension with potential $V$ belonging to certain critical weighted $L^1$ class. Namely, we assume that $\int (1+|x|) |V(x)|dx$ is finite and $H$ has no resonance at zero. In the resonance case we assume $\int (1+|x|^2) |V(x)| dx$ is finite. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/2002.04730v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
