On the Number of Connected Components of the Complement of Limiting Spectrum of Toeplitz Band Matrices

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system’s guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.23671/VNC.2016.2.5917 On the Number of Connected Components of the Complement of Limiting Spectrum of Toeplitz Band Matrices Zolotikh S. A. , Stukopin V. A. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 2. Abstract: 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. Keywords: banded Toeplitz matrices, symbol of the Toeplitz matrix, limiting spectrum, number of connected components. Language: Russian Download the full text For citation: Zolotikh S. A., Stukopin V. A. On the number of connected components of the complement of limiting spectrum of toeplitz band matrices // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 2, pp. 41-48. DOI 10.23671/VNC.2016.2.5917 + References 1. Bottcher A. Ñ., Grudsky S. M. Spectral Properties of Banded Toeplitz Matrices. Philadelphia, SIAM, 2005. 422 с. 2. Batalshchikov A. A., Grudsky S. M., Stukopin V. A. Asymptotics of eigenvalues of symmetric Toeplitz band matrices. Linear Algebra and its Appl., 2015, vol. 469, pp. 464-486. 3. Zolotih S. A., Stukopin V. A. On the Description of the Limiting Spectrum of the Banded Toeplitz Matrices. Matematicheskij forum. T.7. Issledovanija po matematicheskomu analizu. Ser. "Itogi nauki. Jug Rossii" [Mathematical Forum. Vol.7. Studies on Mathematical Analysis. Ser. "Review of Science: The South of Russia"]. Vladikavkaz, SMI VSC RAS, 2013, pp. 80-87 [in Russian]. 4. Schmidt P., Spitzer F. The Toeplitz matrices of an arbitrary Laurent polynomial. Math. Scand., 1960, vol. 8, pp. 15-38. 5. Ullman K. A problem of Schmidt and Spitzer. Bull. Amer. Math. Soc., 1967, vol. 73, pp. 883-885. ← Contents of issue


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