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Spectral Analysis of a Dirac Operator with a Meromorphic Potential
| 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) |
| URI: | http://hdl.handle.net/2115/38256 |
| 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)
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Submitter: 新井 朝雄
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