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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{VMJ_2016_18_2_a4,
     author = {S. A. Zolotykh and V. A. Stukopin},
     title = {On the number of connected components of the complement of limiting spectrum of {Toeplitz} band matrices},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {41--48},
     year = {2016},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a4/}
}
TY  - JOUR
AU  - S. A. Zolotykh
AU  - V. A. Stukopin
TI  - On the number of connected components of the complement of limiting spectrum of Toeplitz band matrices
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 41
EP  - 48
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a4/
LA  - ru
ID  - VMJ_2016_18_2_a4
ER  - 
%0 Journal Article
%A S. A. Zolotykh
%A V. A. Stukopin
%T On the number of connected components of the complement of limiting spectrum of Toeplitz band matrices
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 41-48
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a4/
%G ru
%F VMJ_2016_18_2_a4
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/

[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