Geodesic
On the number of connected components of the complement of limiting spectrum of Toeplitz band matrices
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 41-48 
S. A. Zolotykh; V. A. Stukopin. On the number of connected components of the complement of limiting spectrum of Toeplitz band matrices. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 41-48. http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain lower bounds for the maximum number of connected components of complement of limiting spectrum of Toeplitz band matrix whose symbol is a Laurent polynomial of a given degree. We also give examples of polynomials which are symbols of Toeplitz matrices whose limiting spectrum divides the complex plane into the given number of connected components.

[1] Bottcher A. C., Grudsky S. M., Spectral Properties of Banded Toeplitz Matrices, SIAM, Philadelphia, 2005, 422 pp. | MR | Zbl

[2] Batalshchikov A. A., Grudsky S. M., Stukopin V. A., “Asymptotics of eigenvalues of symmetric Toeplitz band matrices”, Linear Algebra and its Appl., 469 (2015), 464–486 | DOI | MR | Zbl

[3] Zolotykh S. A., Stukopin V. A., “O vychislenii predelnogo spektra lentochnykh tëplitsevykh matrits”, Issledovaniya po mat. analizu, Itogi nauki. Yug Rossii. Mat. forum, 7, YuMI VNTs RAN i RSO-A, Vladikavkaz, 2013, 80–87

[4] Schmidt P., Spitzer F., “The Toeplitz matrices of an arbitrary Laurent polynomial”, Math. Scand., 8 (1960), 15–38 | MR | Zbl

[5] Ullman K., “A problem of Schmidt and Spitzer”, Bull. Amer. Math. Soc., 73 (1967), 883–885 | DOI | MR | Zbl