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 P0, 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

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