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Discreteness of spectrum and strict positivity criteria for magnetic Schrödinger operators | Vladimir Kondratiev
; Vladimir Maz’ya
; Mikhail Shubin
; | Date: |
14 Jun 2002 | Subject: | Spectral Theory; Mathematical Physics MSC-class: 35J10, 35P05, 47F05 | math.SP math-ph math.MP | Affiliation: | Moscow State University), Vladimir Maz’ya (Linköping University), Mikhail Shubin (Northeastern University | Abstract: | 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). | Source: | arXiv, math.SP/0206140 | Services: | Forum | Review | PDF | Favorites |
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