Spectral Problems of a Class of Non-self-adjoint One-dimensional Schrodinger Operators
Spectral Theory
2014-05-13 v3
Abstract
In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q\inL_{1}[0,1] and q_{n}=0 for n=0,-1,-2,..., where q_{n} are the Fourier coefficients of q with respect to the system {e^{i2{\pi}nx}}. We prove that the Bloch eigenvalues are (2{\pi}n+t)^{2} for n\inZ, t\inC and find explicit formulas for the Bloch functions. Then we consider the inverse problem for this operator.
Keywords
Cite
@article{arxiv.1204.3613,
title = {Spectral Problems of a Class of Non-self-adjoint One-dimensional Schrodinger Operators},
author = {O. A. Veliev},
journal= {arXiv preprint arXiv:1204.3613},
year = {2014}
}