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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.
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
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