Spectral distribution results beyond the algebra generated by variable-coefficient Toeplitz sequences: the GLT approach

DOI10.1007/s00041-017-9525-yzbMath1454.15021OpenAlexW2586938515MaRDI QIDQ1746602

Carlo Garoni, Stefano Serra Capizzano

Publication date: 25 April 2018

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-017-9525-y

zbMATH Keywords

eigenvalue distributionapproximating class of sequencesgeneralized convolutiongeneralized locally Toeplitz sequencesingular value distributionvariable-coefficient Toeplitz matrix

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Toeplitz, Cauchy, and related matrices (15B05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On unitarily invariant norms of matrix-valued linear positive operators.
• The GLT class as a generalized Fourier analysis and applications
• Sequences of variable-coefficient Toeplitz matrices and their singular values
• Uniform boundedness of Toeplitz matrices with variable coefficients
• The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
• Locally Toeplitz sequences: Spectral properties and applications
• Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
• Asymptotic behavior of generalized convolutions: an algebraic approach
• Asymptotic invertibility and the collective asymptotic spectral behavior of generalized one-dimensional discrete convolutions
• Szegő-type limit theorems for generalized discrete convolution operators
• Generalized Locally Toeplitz Sequences: Theory and Applications
• Toeplitz matrices with variable coefficients, pseudodifferential operators, and Strichartz's method
• Asymptotic behavior of variable-coefficient Toeplitz determinants
• Distribution results on the algebra generated by Toeplitz sequences: A finite-dimensional approach
• Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients