Pólya's conjecture in the presence of a constant magnetic field

DOI10.4171/JEMS/184zbMath1179.35205arXiv0710.1078OpenAlexW1963765201WikidataQ123315352 ScholiaQ123315352MaRDI QIDQ1041260

Michael Loss, Timo Weidl, Rupert L. Frank

Publication date: 1 December 2009

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.1078

zbMATH Keywords

Laplace operatoreigenvalue boundsmagnetic Schrödinger operatorsPólya's conjecturesemi-classical estimates

Mathematics Subject Classification ID

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

Related Items (18)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions ⋮ Stability and semiclassics in self-generated fields ⋮ Spectral geometry in a rotating frame: properties of the ground state ⋮ Pólya's conjecture for Euclidean balls ⋮ Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem ⋮ Sums of Laplace eigenvalues-rotationally symmetric maximizers in the plane ⋮ Sums of magnetic eigenvalues are maximal on rotationally symmetric domains ⋮ A Lieb–Thirring type inequality for magnetic Schrödinger operators with a radial symmetry ⋮ Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field ⋮ Pólya's conjecture fails for the fractional Laplacian ⋮ Estimates on the eigenvalues of the clamped plate problem on domains in Euclidean spaces ⋮ The Berezin inequality on domains of infinite measure ⋮ Sharp trace asymptotics for a class of \(2D\)-magnetic operators ⋮ Semiclassical bounds in magnetic bottles ⋮ On Riesz Means of Eigenvalues ⋮ A simple proof of Hardy-Lieb-Thirring inequalities ⋮ Magnetic spectral bounds on starlike plane domains

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