Dispersive estimates for fractional order Schrödinger operators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912599662133248 |
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| author | Erdogan, M. Burak Goldberg, Michael Green, William |
| author_facet | Erdogan, M. Burak Goldberg, Michael Green, William |
| contents | We prove dispersive bounds for fractional Schrödinger operators on $\mathbb R^n$ of the form $H=(-Δ)^α+V$ with $V$ a real-valued, decaying potential and $α\notin\mathbb N$. We derive pointwise bounds on the resolvent operators for all $0<α<\frac{n}{2}$, a quantitative limiting absorption principle for $\frac12<α<\frac{n}{2}$, and establish global dispersive estimates in dimension $n\geq 2$ for the range $\frac{n+1}{4}\leq α<\frac{n}2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dispersive estimates for fractional order Schrödinger operators Erdogan, M. Burak Goldberg, Michael Green, William Analysis of PDEs We prove dispersive bounds for fractional Schrödinger operators on $\mathbb R^n$ of the form $H=(-Δ)^α+V$ with $V$ a real-valued, decaying potential and $α\notin\mathbb N$. We derive pointwise bounds on the resolvent operators for all $0<α<\frac{n}{2}$, a quantitative limiting absorption principle for $\frac12<α<\frac{n}{2}$, and establish global dispersive estimates in dimension $n\geq 2$ for the range $\frac{n+1}{4}\leq α<\frac{n}2$. |
| title | Dispersive estimates for fractional order Schrödinger operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.18002 |