Sharp two-sided heat kernel estimates for Schrödinger operators with decaying potentials
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929212934324224 |
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| author | Chen, Xin Wang, Jian |
| author_facet | Chen, Xin Wang, Jian |
| contents | We establish global two-sided heat kernel estimates (for full time and space) of the Schrödinger operator $-\frac{1}{2}Δ+V$ on $\R^d$, where the potential $V(x)$ is locally bounded and behaves like $c|x|^{-α}$ near infinity with $α\in (0,2)$ and $c> 0$, or with $α>0$ and $c<0$.Our results improve all known results in the literature, and it seems that the current paper is the first one where consistent two-sided heat kernel bounds for the long range potentials are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp two-sided heat kernel estimates for Schrödinger operators with decaying potentials Chen, Xin Wang, Jian Analysis of PDEs Probability We establish global two-sided heat kernel estimates (for full time and space) of the Schrödinger operator $-\frac{1}{2}Δ+V$ on $\R^d$, where the potential $V(x)$ is locally bounded and behaves like $c|x|^{-α}$ near infinity with $α\in (0,2)$ and $c> 0$, or with $α>0$ and $c<0$.Our results improve all known results in the literature, and it seems that the current paper is the first one where consistent two-sided heat kernel bounds for the long range potentials are established. |
| title | Sharp two-sided heat kernel estimates for Schrödinger operators with decaying potentials |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2401.09005 |