# Negative Eigenvalues of Two-Dimensional Schrödinger Operators

@article{Grigoryan2011NegativeEO,
title={Negative Eigenvalues of Two-Dimensional Schr{\"o}dinger Operators},
author={Alexander Grigor’yan and Nikolai S. Nadirashvili},
journal={Archive for Rational Mechanics and Analysis},
year={2011},
volume={217},
pages={975-1028}
}
• Published 21 December 2011
• Mathematics
• Archive for Rational Mechanics and Analysis
We prove a certain upper bound for the number of negative eigenvalues of the Schrödinger operator H = −Δ − V in $${\mathbb{R}^{2}.}$$R2.
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Piecewise-polynomial approximation of functions fromHℓ((0, 1)d), 2ℓ=d, and applications to the spectral theory of the Schrödinger operator
For the selfadjoint Schrödinger operator −Δ−αV on ℝ2 the number of negative eigenvalues is estimated. The estimates obtained are based upon a new result on the weightedL2-approximation of functions