On the Singularities of the Magnetic Spectral Shift Function at the Landau Levels期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the Singularities of the Magnetic Spectral Shift Function at the Landau Levels

Authors:	Email author" target="_blank">Claudio?Fernández Email author Email author" target="_blank">Georgi D?Raikov Email author

Institution:	(1) Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile;(2) Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago, Chile

Abstract:	We consider the three-dimensional Schrödinger operators and $H_\pm$ where $H_{0} = (i\nabla + A)^{2} - b$ , A is a magnetic potential generating a constant magnetic field of strength , and $H_{\pm} = H_{0} \pm V$ where $b \geq 0$ decays fast enough at infinity. Then, A. Pushnitskis representation of the spectral shift function (SSF) for the pair of operators $H_\pm, H_0$ is well defined for energies $E \neq 2qb,\, q \in \mathbb{Z}_{+}.$ We study the behaviour of the associated representative of the equivalence class determined by the SSF, in a neighbourhood of the Landau levels $2qb,\, q \in \mathbb{Z}_{+}.$ Reducing our analysis to the study of the eigenvalue asymptotics for a family of compact operators of Toeplitz type, we establish a relation between the type of the singularities of the SSF at the Landau levels and the decay rate of V at infinity. Communicated by Bernard HelfferSubmitted 23/09/03, accepted 15/01/04

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