Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909329636982784 |
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| author | Bogdan, Krzysztof Merz, Konstantin |
| author_facet | Bogdan, Krzysztof Merz, Konstantin |
| contents | Motivated by the study of relativistic atoms, we consider 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 $L^2(\mathbb{R}^d)$, when $κ\geq0$ and $α\in(0,2]\cap(0,d+2\ell)$. We give a ground state representation of the corresponding form on the half-line (Theorem 1.5). For the proof we use subordinated Bessel heat kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00881 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels Bogdan, Krzysztof Merz, Konstantin Analysis of PDEs Mathematical Physics Functional Analysis Motivated by the study of relativistic atoms, we consider 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 $L^2(\mathbb{R}^d)$, when $κ\geq0$ and $α\in(0,2]\cap(0,d+2\ell)$. We give a ground state representation of the corresponding form on the half-line (Theorem 1.5). For the proof we use subordinated Bessel heat kernels. |
| title | Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2305.00881 |