On the Spectrum of an Odd-Order Differential Operator
Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 643-646.

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Operators generated by a differential expression on a finite closed interval are considered. It is shown that, for any odd integer $n$, there exist differential operators of order $n$ whose spectrum fills the whole complex plane.
Keywords: eigenvalues, degenerate boundary conditions, odd-order differential equations.
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A. M. Akhtyamov. On the Spectrum of an Odd-Order Differential Operator. Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 643-646. http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a0/

[1] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, M., 1969 | MR | Zbl

[2] E. A. Shiryaev, A. A. Shkalikov, “Regulyarnye i vpolne regulyarnye differentsialnye operatory”, Matem. zametki, 81:4 (2007), 636–640 | DOI | MR | Zbl

[3] V. A. Sadovnichii, Ya. T. Sultanaev, A. M. Akhtyamov, “General inverse Sturm-Liouville problem with symmetric potential”, Azerb. J. Math., 5:2 (2015), 96–108 | MR | Zbl

[4] V. A. Sadovnichii, B. E. Kanguzhin, “O svyazi mezhdu spektrom differentsialnogo operatora s simmetricheskimi koeffitsientami i kraevymi usloviyami”, Dokl. AN SSSR, 267:2 (1982), 310–313 | MR | Zbl

[5] J. Locker, Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators, Mem. Amer. Math. Soc., 195, no. 911, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[6] A. G. Kurosh, Kurs vysshei algebry, Nauka, M., 1963 | MR