论文信息 - Eigenvalues of Toeplitz matrices in the bulk of the spectrum

Eigenvalues of Toeplitz matrices in the bulk of the spectrum

The authors use results from [6, 7] to analyze the asymptotics of eigenvalues of Toeplitz matrices with certain continuous and discontinuous symbols. In particular, the authors prove a conjecture of Levitin and Shargorodsky on the near-periodicity of Toeplitz eigenvalues.

[1] E. C. OBI. Eigenvalue Distribution of Time and Frequency Limiting , 2007 .

[2] Albrecht Böttcher,et al. Inside the eigenvalues of certain Hermitian Toeplitz band matrices , 2010, J. Comput. Appl. Math..

[3] Aaas News,et al. Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[4] Michael Levitin,et al. Spectral pollution and second-order relative spectra for self-adjoint operators , 2002 .

[5] M. Reed. Methods of Modern Mathematical Physics. I: Functional Analysis , 1972 .

[6] Albrecht Böttcher,et al. Spectral properties of banded Toeplitz matrices , 1987 .

[7] D. Slepian. Some Asymptotic Expansions for Prolate Spheroidal Wave Functions , 1965 .

[8] P. Deift,et al. On the asymptotics of a Toeplitz determinant with singularities , 2012, 1206.1292.

[9] P. Deift,et al. Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities , 2009, 0905.0443.

[10] A. Sobolev,et al. On the near periodicity of eigenvalues of Toeplitz matrices , 2010, 1006.2462.

[11] A. Lenard. Some remarks on large Toeplitz determinants , 1972 .

[12] Michael E. Fisher,et al. Toeplitz Determinants: Some Applications, Theorems, and Conjectures , 2007 .

[13] E. Basor. Trace formulas for Toeplitz matrices with piecewise continuous symbols , 1986 .

[14] A. Böttcher,et al. Introduction to Large Truncated Toeplitz Matrices , 1998 .