Maximum norm versions of the Szegő and Avram-Parter theorems for Toeplitz matrices

DOI10.1016/j.jat.2015.03.003zbMath1320.15028OpenAlexW1979166388MaRDI QIDQ2346289

J. M. Bogoya, Albrecht Böttcher, Egor A. Maksimenko, Sergei M. Grudsky

Publication date: 1 June 2015

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2015.03.003

zbMATH Keywords

eigenvalueToeplitz matrixsingular valueAvram-Parter theoremquantile functionSzegő's theorem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Eigenvalues, singular values, and eigenvectors (15A18) Toeplitz, Cauchy, and related matrices (15B05)

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Cites Work

• Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols
• Inside the eigenvalues of certain Hermitian Toeplitz band matrices
• On the distribution of the singular values of Toeplitz matrices
• On bilinear forms in Gaussian random variables and Toeplitz matrices
• Index calculus for approximation methods and singular value decomposition
• Introduction to large truncated Toeplitz matrices
• A note on singular values of Cauchy-Toeplitz matrices
• A unifying approach to some old and new theorems on distribution and clustering
• Structured condition numbers of large Toeplitz matrices are rarely better than usual condition numbers
• Asymptotic Statistics
• A Finer Aspect of Eigenvalue Distribution of Selfadjoint Band Toeplitz Matrices
• Piecewise Continuous Toeplitz Matrices and Operators: Slow Approach to Infinity
• An Elementary View of Weyl’s Theory of Equal Distribution
• Eigenvalues of Toeplitz matrices in the bulk of the spectrum
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