It is wellknown that the spectral theory of operators with a complex 1-periodic potential can be reduced to the study of operators , which are defined by the -periodic boundary conditions and . For the spectral expansion, the authors determine first the asymptotics of the eigenvalues and eigenfunctions of the operators , , . Their key result is the estimate
on the eigenfunctions. This is used to show that and the associated functions form a Riesz basis of by constructing a biorthonormal system with eigenfunctions of . Using this result, a spectral representation of functions with compact support can be derived.