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

2003/08/27 by Kwang C. Shin
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as Math. Nachr. 261-262: 171-175 (2003) · 6 pages; no figure; to appear in Math. Nachr

arxiv created 2003/08/27 · arxiv updated 2009/12/01

Abstract

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

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