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

*λ*and if_{0,1}∈ ℝ*u,v*solve the Dirac equation*H u= λ*,_{0}u*H v= λ*(in the weak sense) and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection_{1}v*P*equals the number of zeros of the Wronskian of_{(λ0, λ1)}(H)*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