Intrinsic ultracontractivity for Schrödinger semigroups based on cylindrical fractional Laplacian on the plane
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910535272890368 |
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| author | Kulczycki, Tadeusz Sztonyk, Kinga |
| author_facet | Kulczycki, Tadeusz Sztonyk, Kinga |
| contents | We study Schrödinger operators on $\mathbb{R}^2$ $$ H = \left(-\frac{\partial^2}{\partial x_1^2}\right)^{α/2} + \left(-\frac{\partial^2}{\partial x_2^2}\right)^{α/2} + V, $$ for $α\in (0,2)$ and some sufficiently regular, radial, confining potentials $V$. We obtain necessary and sufficient conditions on intrinsic ultracontractivity for semigroups $\{e^{-tH}: \, t \ge 0\}$. We also get sharp estimates of first eigenfunctions of $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intrinsic ultracontractivity for Schrödinger semigroups based on cylindrical fractional Laplacian on the plane Kulczycki, Tadeusz Sztonyk, Kinga Probability Mathematical Physics We study Schrödinger operators on $\mathbb{R}^2$ $$ H = \left(-\frac{\partial^2}{\partial x_1^2}\right)^{α/2} + \left(-\frac{\partial^2}{\partial x_2^2}\right)^{α/2} + V, $$ for $α\in (0,2)$ and some sufficiently regular, radial, confining potentials $V$. We obtain necessary and sufficient conditions on intrinsic ultracontractivity for semigroups $\{e^{-tH}: \, t \ge 0\}$. We also get sharp estimates of first eigenfunctions of $H$. |
| title | Intrinsic ultracontractivity for Schrödinger semigroups based on cylindrical fractional Laplacian on the plane |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2407.14325 |