• Corpus ID: 118018443

# On negative eigenvalues of low-dimensional Schr\"{o}dinger operators

@article{Molchanov2011OnNE,
title={On negative eigenvalues of low-dimensional Schr\"\{o\}dinger operators},
author={Stanislav Molchanov and Boris Vainberg},
journal={arXiv: Mathematical Physics},
year={2011}
}
• Published 4 May 2011
• Mathematics
• arXiv: Mathematical Physics
The paper concerns upper and lower estimates for the number of negative eigenvalues of one- and two-dimensional Schr\"{o}dinger operators and more general operators with the spectral dimensions $d\leq 2$. The classical Cwikel-Lieb-Rosenblum (CLR) upper estimates require the corresponding Markov process to be transient, and therefore the dimension to be greater than two. We obtain CLR estimates in low dimensions by transforming the underlying recurrent process into a transient one using partial…
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These classical inequalities allow one to estimate the number of negative eigenvalues and the sums $$S_\gamma = \sum { |\lambda _i |^\gamma }$$ for a wide class of Schrodinger operators. We provide
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The purpose of this talk is to present a certain method of obtaining upper estimates of eigenvalues of Schrodinger type operators on Riemannian manifolds, which was introduced in the paper Grigor’yan
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