Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. A. Naimark, Linear Differential Operators (Nauka, Moscow, 1969) [in Russian].
E. A. Shiryaev and A. A. Shkalikov, “Regular and completely regular differential operators,” Mat. Zametki 81 (4), 636–640 (2007) [Math. Notes 81 (3–4), 566–570 (2007)].
V. A. Sadovnichii, Ya. T. Sultanaev, and A. M. Akhtyamov, “General inverse Sturm–Liouville problem with symmetric potential,” Azerb. J. Math. 5 (2), 96–108 (2015).
V. A. Sadovnichii and B. E. Kanguzhin, “A connection between the spectrum of a differential operator with symmetric coefficients and the boundary conditions,” Dokl. Akad. Nauk SSSR 267 (2), 310–313 (1982) [SovietMath. Dokl. 26, 614–618 (1982)].
J. Locker, Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators, in Mem. Amer. Math. Soc. (Amer. Math. Soc., Providence, RI, 2008), Vol. 195, No. 911.
A. G. Kurosh, A Course in Higher Algebra (Nauka, Moscow, 1963) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A. M. Akhtyamov, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 5, pp. 643–646.
Rights and permissions
About this article
Cite this article
Akhtyamov, A.M. On the spectrum of an odd-order differential operator. Math Notes 101, 755–758 (2017). https://doi.org/10.1134/S0001434617050017
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434617050017