open access

https://hdl.handle.net/2115/38256

Spectral Analysis of a Dirac Operator with a Meromorphic Potential

英語

2005-06-15

Academic Press

Journal of Mathematical Analysis and Applications

306(2)

440-461

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).

学術雑誌論文

Accepted Manuscript

0022-247X

AA00252847