On the spectrality and spectral expansion of the non-self-adjoint mathieu-hill operator in L2(−∞,∞)
MetadataShow full item record
CitationVeliev, O. (2020). On the spectrality and spectral expansion of the non-self-adjoint mathieu-hill operator in L2(−∞,∞). Communications on Pure and Applied Analysis, 19(3), 1537-1562. http://dx.doi.org/10.3934/cpaa.2020077
In this paper we investigate the non-self-adjoint operator H generated in L-2(-infinity, infinity) 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.