Discreteness of spectrum and strict positivity criteria for magnetic Schrödinger operators

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We establish necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schrödinger operators with a positive scalar potential. They are expressed in terms of Wiener's capacity and the local energy of the magnetic field. The conditions for the discreteness of spectrum depend on two functional parameters. One of them is a decreasing function of one variable whose argument is the normalized local energy of the magnetic field. This function enters the negligibility condition of sets for the scalar potential. We give a description for the range of admissible functional parameters which is precise in a certain sense. In case when there is no magnetic field, our results extend the discreteness of spectrum and positivity criteria by A.Molchanov (1953) and V.Maz'ya (1973).
Final version, a small error corrected. To appear in Communications in Partial Differential Equations, v. 29, no. 3 & 4 (2004), 489-521

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Spectral Theory, Mathematical Physics, 35J10, 35P05, 47F05

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http://salesiana.dossiersoluciones.com/handle/123456789/95900

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206140
 http://arxiv.org/abs/math/0206140
 Commun. Partial Diff. Equations, v. 29 (2004), 489-521

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arXiv