On half-line spectra for a class of non-self-adjoint Hill operators

Details On half-line spectra for a class of non-self-adjoint Hill operators On half-line spectra for a class of non-self-adjoint Hill operators

2003-08-27

arxiv.org/abs/math-ph/0308032v1

Math. Nachr. 261-262: 171-175 (2003)

Physics

Mathematical Physics

6 pages; no figure; to appear in Math. Nachr

Scientific paper

In 1980, Gasymov showed that non-self-adjoint Hill operators with
complex-valued periodic potentials of the type $V(x)=\sum_{k=1}^{\infty} a_k
e^{ikx}$, with $\sum_{k=1}^{\infty}|a_k|<\infty$, have spectra $[0, \infty)$.
In this note, we provide an alternative and elementary proof of this result.

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