On the Spectrality and Spectral Expansion of the Non-self-adjoint Mathieu-Hill Operator in All Real Line
arXiv:1906.04912
Abstract
In this paper we investigate the non-self-adjoint operator H generated in all real line by the Mathieu-Hill equation with a complex-valued potential. We find a necessary and sufficient conditions on the potential for which H has no spectral singularity at infinity and it is an asymptotically spectral operator. Moreover, we give a detailed classification, stated in term of the potential, for the form of the spectral decomposition of the operator H by investigating the essential spectral singularities.
arXiv admin note: substantial text overlap with arXiv:1202.4735