Lieb-Thirring inequalities on the spheres and $SO(3)$
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| Format: | Preprint |
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2024
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| _version_ | 1866910527711608832 |
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| author | Kowacs, André Pedroso Ruzhansky, Michael |
| author_facet | Kowacs, André Pedroso Ruzhansky, Michael |
| contents | In this paper, we obtain new upper bounds for the Lieb-Thirring inequality on the spheres of any dimension greater than $2$. As far as we have checked, our results improve previous results found in the literature for all dimensions greater than $2$. We also prove and exhibit an explicit new upper bound for the Lieb-Thirring inequality on $SO(3)$. We also discuss these estimates in the case of general compact Lie groups. Originally developed for estimating the sums of moments of negative eigenvalues of the Schrödinger operator in $L^2(\mathbb{R}^n)$, these inequalities have applications in quantum mechanics and other fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15134 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lieb-Thirring inequalities on the spheres and $SO(3)$ Kowacs, André Pedroso Ruzhansky, Michael Spectral Theory Functional Analysis Primary: 26D10. Secondary: 22E30 In this paper, we obtain new upper bounds for the Lieb-Thirring inequality on the spheres of any dimension greater than $2$. As far as we have checked, our results improve previous results found in the literature for all dimensions greater than $2$. We also prove and exhibit an explicit new upper bound for the Lieb-Thirring inequality on $SO(3)$. We also discuss these estimates in the case of general compact Lie groups. Originally developed for estimating the sums of moments of negative eigenvalues of the Schrödinger operator in $L^2(\mathbb{R}^n)$, these inequalities have applications in quantum mechanics and other fields. |
| title | Lieb-Thirring inequalities on the spheres and $SO(3)$ |
| topic | Spectral Theory Functional Analysis Primary: 26D10. Secondary: 22E30 |
| url | https://arxiv.org/abs/2406.15134 |