Invariance of intrinsic hypercontractivity under perturbation of Schrödinger operators
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915302708609024 |
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| author | Gross, Leonard |
| author_facet | Gross, Leonard |
| contents | A Schrödinger operator that is bounded below and has a unique positive ground state can be transformed into a Dirichlet form operator by the ground state transformation. If the resulting Dirichlet form operator is hypercontractive, Davies and Simon call the Schrödinger operator ``intrinsically hypercontractive". I will show that if one adds a suitable potential onto an intrinsically hypercontractive Schrödinger operator it remains intrinsically hypercontractive. The proof uses a fortuitous relation between the WKB equation and logarithmic Sobolev inequalities. All bounds are dimension independent. The main theorem will be applied to several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20282 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariance of intrinsic hypercontractivity under perturbation of Schrödinger operators Gross, Leonard Mathematical Physics Functional Analysis 81Q15, 47D08 (Primary), 35J10, 35B20, 60J46 (Secondary) A Schrödinger operator that is bounded below and has a unique positive ground state can be transformed into a Dirichlet form operator by the ground state transformation. If the resulting Dirichlet form operator is hypercontractive, Davies and Simon call the Schrödinger operator ``intrinsically hypercontractive". I will show that if one adds a suitable potential onto an intrinsically hypercontractive Schrödinger operator it remains intrinsically hypercontractive. The proof uses a fortuitous relation between the WKB equation and logarithmic Sobolev inequalities. All bounds are dimension independent. The main theorem will be applied to several examples. |
| title | Invariance of intrinsic hypercontractivity under perturbation of Schrödinger operators |
| topic | Mathematical Physics Functional Analysis 81Q15, 47D08 (Primary), 35J10, 35B20, 60J46 (Secondary) |
| url | https://arxiv.org/abs/2412.20282 |