Hill's operators with the potentials analytically dependent on energy
Mathematical Physics
2020-06-03 v1 math.MP
Abstract
We consider Schr\"odinger operators on the line with potentials that are periodic with respect to the coordinate variable and real analytic with respect to the energy variable. We prove that if the imaginary part of the potential is bounded in the right half-plane, then the high energy spectrum is real, and the corresponding asymptotics are determined. Moreover, the Dirichlet and Neumann problems are considered. These results are used to analyze the good Boussinesq equation.
Cite
@article{arxiv.2006.01566,
title = {Hill's operators with the potentials analytically dependent on energy},
author = {Andrey Badanin and Evgeny L. Korotyaev},
journal= {arXiv preprint arXiv:2006.01566},
year = {2020}
}
Comments
23 pages, 1 figure