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Spectral Analysis of a Dirac Operator with a Meromorphic Potential

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Title: Spectral Analysis of a Dirac Operator with a Meromorphic Potential
Authors: Arai, Asao Browse this author →KAKEN DB
Hayashi, Kunimitsu Browse this author
Issue Date: 15-Jun-2005
Publisher: Academic Press
Journal Title: Journal of Mathematical Analysis and Applications
Volume: 306
Issue: 2
Start Page: 440
End Page: 461
Publisher DOI: 10.1016/j.jmaa.2005.01.001
Abstract: We consider an operator Q(V) of Dirac type with a meromorphic potential given in terms of a function V of the form V(z) = λV1(z) + μV2(z), z ∈ C \ {0}, where V1 is a complex polynomial of 1/z, V2 is a polynomial of z, and λ and μ are non-zero complex parameters. The operator Q(V) acts in the Hilbert space L^2(IR^2;C^4) = ⊕^4L^2(IR^2). The main results we prove include: (i) the (essential) self-adjointness of Q(V); (ii) the pure discreteness of the spectrum of Q(V) ; (iii) if V1(z) = z^[-p] and 4 ≤ degV2 ≤ p + 2, then kerQ(V) ≠ {0} and dim kerQ(V) is independent of (λ, μ) and lower order terms of ∂V2/∂z; (iv) a trace formula for dim kerQ(V).
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 新井 朝雄

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