$L^p$-continuity of wave operators for higher order Schr\'odinger operators with threshold eigenvalues in high dimensions
| Autor: | Erdogan, M. Burak, Green, William R., LaMaster, Kevin |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider the higher order Schr\"odinger operator $H=(-\Delta)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>4m$, $m\in \mathbb N$. We adapt our recent results for $m>1$ to show that when $H$ has a threshold eigenvalue the wave operators are bounded on $L^p(\mathbb R^n)$ for the natural range $1\leq p<\frac{n}{2m}$ in both even and odd dimensions. The approach used works without distinguishing even and odd cases, and matches the range of boundedness in the classical case when $m=1$. The proof applies in the classical $m=1$ case as well and simplifies the argument. Comment: 23 pages. arXiv admin note: text overlap with arXiv:2207.14264 |
| Databáze: | arXiv |
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