The Szegő and Avram-Parter theorems for general test functions

DOI10.1016/j.crma.2008.06.002zbMath1145.15007OpenAlexW2115605241MaRDI QIDQ935356

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

Publication date: 6 August 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.06.002

zbMATH Keywords

eigenvaluesarithmetic meansingular valuesToeplitz matricesSzegő theoremtest functionsHermitian Toeplitz matricesAvram-Parter theorems

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (4)

The part of my path I walked together with Sergei Grudsky ⋮ A note on the (regularizing) preconditioning of \(g\)-Toeplitz sequences via \(g\)-circulants ⋮ Asymptotics of eigenvalues of symmetric Toeplitz band matrices ⋮ The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction

Cites Work

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• On unitarily invariant norms of matrix-valued linear positive operators.
• Some Problems Concerning the Test Functions in the Szegö and Avram-Parter Theorems
• Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function
• A note on the spectral distribution of toeplitz matrices

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