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

✍ Scribed by Kwang C. Shin

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
102 KB
Volume
261-262
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In 1980, Gasymov showed that non‐self‐adjoint Hill operators with complex‐valued periodic potentials of the type $ V(x) = \sum ^{\infty} _{k=1} a_{k} e^{ikx} $, with $ \sum ^{\infty} _{k=1} \vert a_{k} \vert < \infty $, have spectra [0, ∞). In this note, we provide an alternative and elementary proof of this result. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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