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The construction of self-adjoint operators of Hill with periodic eigenfunctions

✍ Scribed by F. Poleunis; O. Leroy

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
501 KB
Volume
3
Category
Article
ISSN
0377-0427

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✦ Synopsis

We find necessary and sufficient conditions to guarantee the existence resp. coexistence of linear independent periodic zero-elements of period m~, m β€’ IN, of Hill's differential operator D2 + Q, with co being the minimal period of the function Q. These conditions enable us to construct an unbounded self-adjoint operator which only has periodic eigenfunctions with prescribed period.

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On half-line spectra for a class of non-self-adjoint Hill operators
✍ Kwang C. Shin πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 102 KB πŸ‘ 1 views

## 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