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Global solvability on the torus for certain classes of formally self-adjoint operators

✍ Scribed by Gerson Petronilho

Publisher: Springer
Year: 2000
Tongue: English
Weight: 79 KB
Volume: 103
Category: Article
ISSN: 0025-2611
DOI: 10.1007/s002290070025

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## 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 an