On the spectral singularities and spectrality of the Hill operator (Q2807237)

The author continues his investigations of the spectrality of the Hill operator \(L(q)\) with a complex-valued potential \(q\). A central result is that the following statements are equivalent: (i) \(L(q)\) has no spectral singularities at infinity. (ii) \(L(q)\) is an asymptotically spectral operator. In fact, he shows that (i) as well as (ii) are equivalent to a third statement which is more convenient to exploit later in the paper, but which is technically too involved to reproduce here. In case (i) holds, an expansion theorem is given involving like its classical counterpart the canonical fundamental system of the equation and the discriminant associated with it.