Negative eigenvalues of two-dimensional Schrödinger operators

DOI10.1007/s00205-015-0848-zzbMath1319.35128arXiv1112.4986OpenAlexW2077577317MaRDI QIDQ2354699

Alexander Grigor'yan, Nikolai S. Nadirashvili

Publication date: 20 July 2015

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.4986

zbMATH Keywords

eigenvaluesSchrödinger-type operator

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Schrödinger operator, Schrödinger equation (35J10)

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Cites Work

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• On spectral estimates for Schrödinger-type operators: the case of small local dimension
• On spectral estimates for two-dimensional Schrödinger operators
• On the negative spectrum of the two-dimensional Schrödinger operator with radial potential
• On the Schrödinger equation and the eigenvalue problem
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator
• The Rozenblum-Lieb-Cwikel inequality for Markov generators
• Regular and pathological eigenvalue behavior for the equation \(-\lambda u=Vu\) on the semiaxis
• The uncertainty principle
• SOME ELEMENTARY INEQUALITIES
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• On the Eigenvalue Behaviour for a Class of Differential Operators on Semiaxis
• Spectral Estimates for Magnetic Operators.
• Isoperimetric properties of higher eigenvalues of elliptic operators
• Bound states in one and two spatial dimensions
• [https://portal.mardi4nfdi.de/wiki/Publication:4893803 The negative discrete spectrum of a two-dimensional Schr�dinger operator]
• On General Cwikel–Lieb–Rozenblum and Lieb–Thirring Inequalities
• PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$
• A Weak Parallelogram Law for l p
• The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius

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