Trace formulas and a Borg‐type theorem for CMV operators with matrix‐valued coefficients

DOI10.1002/mana.200810207zbMath1186.47029arXiv0808.0382OpenAlexW2963140617MaRDI QIDQ5188002

Maxim Zinchenko

Publication date: 10 March 2010

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.0382

zbMATH Keywords

inverse spectral problemreflectionlessblock CMV matricesBorg-type theoremmatrix-valued Verblunsky coefficients

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) Inverse problems involving ordinary differential equations (34A55) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Cites Work

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• Analogs of the \(m\)-function in the theory of orthogonal polynomials on the unit circle
• On isospectral sets of Jacobi operators
• The recurrent Hill's equation
• Perturbations of orthogonal polynomials with periodic recursion coefficients
• The Floquet exponent for two-dimensional linear systems with bounded coefficients
• Almost periodicity of some random potentials
• Schur parameter pencils for the solution of the unitary eigenproblem
• Trace formulas and inverse spectral theory for Jacobi operators
• An inverse problem associated with polynomials orthogonal on the unit circle
• Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions
• A difference equation arising from the trigonometric moment problem having random reflection coefficients -- an operator theoretic approach
• Spectral analysis of unitary band matrices
• Asymptotic behavior of polynomials orthonormal on a homogeneous set
• Borg-type theorems for matrix-valued Schrödinger operators
• Rotation number associated with difference equations satisfied by polynomials orthogonal on the unit circle
• The trace formula for Schrödinger operators on the line
• Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
• Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum
• On Borg-type theorems for first-order systems on a finite interval
• Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
• Weyl--Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle
• Algebro-geometric solutions of the Baxter-Szegő difference equation
• Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators
• On the trigonometric moment problem
• The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy
• The Analytic Theory of Matrix Orthogonal Polynomials
• A systematic approach to the soliton equations of a discrete eigenvalue problem
• Nonlinear differential−difference equations
• Nonlinear differential–difference equations and Fourier analysis
• A Nonlinear Difference Scheme and Inverse Scattering
• A unitary invariant for pairs of self-adjoint operators.
• On the Solution of a Class of Nonlinear Partial Difference Equations
• On Matrix-Valued Herglotz Functions
• Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators
• Functional representation of the Ablowitz-Ladik hierarchy
• The Borg theorem for the vectorial Hill's equation
• Finite genus solutions to the Ablowitz‐Ladik equations
• CMV: The unitary analogue of Jacobi matrices
• Algebro-Geometric Finite-Band Solutions of the Ablowitz-Ladik Hierarchy
• Weyl-Titchmarsh theory and Borg-Marchenko-type uniqueness results for CMV operators with matrix-valued Verblunsky coefficients
• CMV matrices in random matrix theory and integrable systems: a survey
• Circular parameters of polynomials orthogonal on several arcs of the unit circle
• Szegö difference equations, transfer matrices and orthogonal polynomials on the unit circle