Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866916330555310080 |
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| author | Dicke, Alexander Seelmann, Albrecht Veselic, Ivan |
| author_facet | Dicke, Alexander Seelmann, Albrecht Veselic, Ivan |
| contents | We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of Shubin-type. The sensor sets are allowed to decay exponentially, where the precise allowed decay rate depends on the potential. The proof uses an interpolation inequality derived by Carleman estimates, quantitative weighted $L^2$-estimates and an $H^1$-concentration estimate, all of them for functions in a spectral subspace of the operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08682 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials Dicke, Alexander Seelmann, Albrecht Veselic, Ivan Analysis of PDEs 35Pxx (Primary), 35J10, 35B40 (Secondary) We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of Shubin-type. The sensor sets are allowed to decay exponentially, where the precise allowed decay rate depends on the potential. The proof uses an interpolation inequality derived by Carleman estimates, quantitative weighted $L^2$-estimates and an $H^1$-concentration estimate, all of them for functions in a spectral subspace of the operator. |
| title | Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials |
| topic | Analysis of PDEs 35Pxx (Primary), 35J10, 35B40 (Secondary) |
| url | https://arxiv.org/abs/2206.08682 |