Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator
We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schr\"odinger operator \(-\Delta - (d-2)^2/(4|x|^2) -W(x)\) on \(L^2(\mathbb{R}^d)\). The bound is given in terms of a weighted \(L^{d/2}-\)norm of \(W\) which is sharp in both large and small c...
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Published in | arXiv.org |
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Main Authors | , , , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
19.06.2024
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Subjects | |
Online Access | Get full text |
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Summary: | We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schr\"odinger operator \(-\Delta - (d-2)^2/(4|x|^2) -W(x)\) on \(L^2(\mathbb{R}^d)\). The bound is given in terms of a weighted \(L^{d/2}-\)norm of \(W\) which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian. |
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ISSN: | 2331-8422 |