On the simplicity of the eigenvalues of non-self-adjoint mathieu-hill operators

Abstract

Firstly, we analyze some spectral properties of the non-self-adjoint Hill operator with piecewise continuous even potential. Then using this we find conditions on the potential of the non-self-adjoint Mathieu operator, such that all eigenvalues of the periodic, antiperiodic, Dirichlet, and Neumann boundary value problems are simple.