  By the introduction of a generalized Evans function defined by an appropriate
2-modified Fredholm determinant, we give a simple proof of convergence in
location and multiplicity of Hill's method for numerical approximation of
spectra of periodic-coefficient ordinary differential operators. Our results
apply to operators of nondegenerate type, under the condition that the
principal coefficient matrix be symmetric positive definite (automatically
satisfied in the scalar case). Notably, this includes a large class of
nonselfadjoint operators, which were previously not treated. The case of
general coefficients depends on an interesting operator-theoretic question
regarding properties of Toeplitz matrices.
