Spectral Analysis of the Non-self-adjoint Mathieu-Hill Operator
Spectral Theory
2017-04-04 v5
Abstract
We obtain uniform, with respect to t asymptotic formulas for the eigenvalues of the operators generated in (0,1) by the Mathieu-Hill equation with a complex-valued potential and by the t-periodic boundary conditions. Then using it we investigate the non-self-adjoint Mathieu-Hill operator H generated in the allreal line by the same equation and establish the necessary and sufficient conditions for the potential for which H has no spectral singularity at infinity and it is an asymptotically spectral operator.
Keywords
Cite
@article{arxiv.1202.4735,
title = {Spectral Analysis of the Non-self-adjoint Mathieu-Hill Operator},
author = {O. A. Veliev},
journal= {arXiv preprint arXiv:1202.4735},
year = {2017}
}