Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915335138967552 |
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| author | Bogdan, Krzysztof Merz, Konstantin |
| author_facet | Bogdan, Krzysztof Merz, Konstantin |
| contents | Motivated by the study of relativistic atoms, we prove sharp heat kernel bounds for the Hardy operator $(-Δ)^{α/2}-κ|x|^{-α}$ acting on functions of the form $u(|x|) |x|^{\ell} Y_{\ell,m}(x/|x|)$ in $L^2(\R^d)$, when $α\in(0,2]\cap(0,d+2\ell)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels Bogdan, Krzysztof Merz, Konstantin Analysis of PDEs Functional Analysis Probability Motivated by the study of relativistic atoms, we prove sharp heat kernel bounds for the Hardy operator $(-Δ)^{α/2}-κ|x|^{-α}$ acting on functions of the form $u(|x|) |x|^{\ell} Y_{\ell,m}(x/|x|)$ in $L^2(\R^d)$, when $α\in(0,2]\cap(0,d+2\ell)$. |
| title | Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels |
| topic | Analysis of PDEs Functional Analysis Probability |
| url | https://arxiv.org/abs/2506.08115 |