Spectral asymptotics for Kac-Murdock-Szegő matrices

DOI10.1007/s11537-018-1640-2zbMath1395.15023arXiv1610.00084OpenAlexW2529436292MaRDI QIDQ1744821

Tyler McMillen, Allen Alvarez Loya, Alain Bourget

Publication date: 19 April 2018

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.00084

zbMATH Keywords

Schrödinger operatorToeplitz matrixKac-Murdock-Szegő matrixSzegő's limit theorem

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) 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)

Related Items (4)

The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument ⋮ Asymptotic root distribution of Charlier polynomials with large negative parameter ⋮ Spectral distribution of families of Hankel matrices ⋮ Localization and Pseudospectra of Twisted Toeplitz Matrices with Applications to Ion Channels

Uses Software

• Eigtool

Cites Work

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• The theory of locally Toeplitz sequences: a review, an extension, and a few representative applications
• On certain Toeplitz-like matrices and their relation to the problem of lattice vibrations
• A first Szegő's limit theorem for a class of non-Toeplitz matrices
• Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
• Spectral analysis and structure preserving preconditioners for fractional diffusion equations
• On the eigenvalues of double band matrices
• The GLT class as a generalized Fourier analysis and applications
• The structured distance to normality of banded Toeplitz matrices
• Toeplitz matrices and determinants with Fisher-Hartwig symbols
• On the distribution of the singular values of Toeplitz matrices
• On bilinear forms in Gaussian random variables and Toeplitz matrices
• Asymptotic behavior of block Toeplitz matrices and determinants. II
• A trace formula for variable-coefficient Toeplitz matrices with symbols of bounded variation
• The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
• Locally Toeplitz sequences: Spectral properties and applications
• Spectral distribution of generalized Kac-Murdock-Szegö matrices
• Asymptotics of determinants of discrete Schrödinger operators
• A trace formula for a class of variable-coefficient block Toeplitz matrices
• Some results on complex Toeplitz eigenvalues
• Asymptotic behavior of block Toeplitz matrices and determinants
• Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
• On the singular values of generalized Toeplitz matrices
• A unifying approach to some old and new theorems on distribution and clustering
• Spectral density of Jacobi matrices with small deviations
• An exercise(?) in Fourier analysis on the Heisenberg group
• Eigenvalue distributions of large Hermitian matrices; Wigner's semi- circle law and a theorem of Kac, Murdock, and Szegö
• On the zeros of complex Van Vleck polynomials
• On spectral polynomials of the Heun equation. II
• Root asymptotics of spectral polynomials for the Lamé operator
• The spectra of certain Toeplitz matrices
• Asymptotic behaviour of class of determinants
• The structured distance to normality of Toeplitz matrices with application to preconditioning
• On the determinants of certain Toeplitz matrices
• The Toeplitz Matrices of an Arbitrary Laurent Polynomial.
• New identities for the spectrum of the quantum Euler top
• Spectral inequalities for the quantum asymmetric top
• A TRACE FORMULA FOR A FAMILY OF JACOBI OPERATORS
• A continuum limit of the Toda lattice
• Wave packet pseudomodes of twisted Toeplitz matrices
• Useful Bounds on the Extreme Eigenvalues and Vectors of Matrices for Harper’s Operators
• The semiclassical density of states for the quantum asymmetric top
• A problem of Schmidt and Spitzer
• Spectral Properties of Banded Toeplitz Matrices
• On the Eigenvalues of Generalized Toeplitz Matrices.
• A note on the asymptotic spectra of finite difference discretizations of second order elliptic partial differential equations
• Asymptotic behavior of variable-coefficient Toeplitz determinants
• Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients

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