Article
Proc. Amer. Math. Soc. 126, 1685-1695 (1998)
[DOI: 10.1090/S0002-9939-98-04310-X]
Renormalized Oscillation Theory for Dirac Operators
Gerald Teschl
Oscillation theory for one-dimensional Dirac operators with separated boundary
conditions is investigated. Our main theorem reads: If λ0,1∈ ℝ
and if u,v solve the Dirac equation H u= λ0 u, H v= λ1 v (in
the weak sense) and respectively satisfy the boundary condition on the left/right,
then the dimension of the spectral projection P(λ0, λ1)(H)
equals the number of zeros of the Wronskian of u and v. As an application we
establish finiteness of the number of eigenvalues in essential spectral gaps of
perturbed periodic Dirac operators.
MSC91: Primary 36C10, 39L40; Secondary 34B24, 34L15
Keywords: Oscillation theory, Dirac operators, spectral theory
Download