Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions

L. Erdös, Annales de l’Institut Fourier 52 (2002) 1833–1874+XI+VII.

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Abstract
We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface M is bounded by the L1-norm of the magnetic field B. This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with ∫M |B| even in case of the trivial bundle.
Publishing Year
Date Published
2002-01-01
Journal Title
Annales de l'Institut Fourier
Volume
52
Issue
6
Page
1833 - 1874+XI+VII
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Erdös L. Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions. Annales de l’Institut Fourier. 2002;52(6):1833-1874+XI+VII. doi:10.5802/aif.1936
Erdös, L. (2002). Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions. Annales de l’Institut Fourier, 52(6), 1833–1874+XI+VII. https://doi.org/10.5802/aif.1936
Erdös, László. “Spectral Shift and Multiplicity of the First Eigenvalue of the Magnetic Schrödinger Operator in Two Dimensions.” Annales de l’Institut Fourier 52, no. 6 (2002): 1833–1874+XI+VII. https://doi.org/10.5802/aif.1936.
L. Erdös, “Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions,” Annales de l’Institut Fourier, vol. 52, no. 6, p. 1833–1874+XI+VII, 2002.
Erdös L. 2002. Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions. Annales de l’Institut Fourier. 52(6), 1833–1874+XI+VII.
Erdös, László. “Spectral Shift and Multiplicity of the First Eigenvalue of the Magnetic Schrödinger Operator in Two Dimensions.” Annales de l’Institut Fourier, vol. 52, no. 6, Association des Annales de l’Institut Fourier, 2002, p. 1833–1874+XI+VII, doi:10.5802/aif.1936.

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