Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503087 | Journal of Mathematical Analysis and Applications | 2005 | 22 Pages |
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), zâCâ{0}, where V1 is a complex polynomial of 1/z, V2 is a polynomial of z, and λ and μ are nonzero complex parameters. The operator Q(V) acts in the Hilbert space L2(R2;C4)=â4L2(R2). 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)=zâp and 4⩽degV2⩽p+2, then kerQ(V)â {0} and dimkerQ(V) is independent of (λ,μ) and lower order terms of âV2/âz; (iv) a trace formula for dimkerQ(V).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Asao Arai, Kunimitsu Hayashi,