2024-03-29T08:01:47Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/382562022-11-17T02:08:08Zhdl_2115_20039hdl_2115_116Spectral Analysis of a Dirac Operator with a Meromorphic Potential1000080134807Arai, AsaoHayashi, Kunimitsuopen access421We 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).Academic Press2005-06-15engjournal articleAMhttp://hdl.handle.net/2115/38256https://doi.org/10.1016/j.jmaa.2005.01.0010022-247XAA00252847Journal of Mathematical Analysis and Applications3062440461https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/38256/1/ArHa.pdfapplication/pdf143.89 KB2005-06-15