Analogs of the \(m\)-function in the theory of orthogonal polynomials on the unit circle

DOI10.1016/j.cam.2004.01.022zbMath1055.33010arXivmath/0311050OpenAlexW2044340537MaRDI QIDQ596255

Barry Simon

Publication date: 10 August 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311050

zbMATH Keywords

Szegő functionWeyl-Titchmarsh \(m\)-functionorthogonal polynomials on the unit circleVerblunsky coefficientsCarathéodory and Schur functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items

Discrete self-adjoint Dirac systems: asymptotic relations, Weyl functions and Toeplitz matrices, Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line, Weyl--Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle, Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators, A condition for purely absolutely continuous spectrum for CMV operators using the density of states, Wall polynomials on the real line: a classical approach to OPRL Khrushchev's formula, Absence of singular continuous spectrum for perturbed discrete Schrödinger operators, Dissipative operator and its Cayley transform, Generalized Kotani's trick for unitary operators, A new method for dissipative dynamic operator with transmission conditions, Essential closures and AC spectra for reflectionless CMV, Jacobi, and Schrödinger operators revisited, Purely singular continuous spectrum for limit-periodic CMV operators with applications to quantum walks, On a completely non-unitary contraction and associated dissipative difference operator, Trace formulas and a Borg‐type theorem for CMV operators with matrix‐valued coefficients, Revisiting the Christ–Kiselev’s multi-linear operator technique and its applications to Schrödinger operators, Algebro-geometric solutions of the Baxter-Szegő difference equation, Subordinacy theory for extended CMV matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cesàro asymptotics for orthogonal polynomials on the unit circle and classes of measures
• Classification theorems for general orthogonal polynomials on the unit circle
• Kotani theory for one dimensional stochastic Jacobi matrices
• A difference equation arising from the trigonometric moment problem having random reflection coefficients -- an operator theoretic approach
• Sum rules for Jacobi matrices and their applications to spectral theory
• Sum rules and the Szegő condition for orthogonal polynomials on the real line
• A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure
• A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices
• A special class of polynomials orthogonal on the unit circle including the associated polynomials
• A new approach to inverse spectral theory. I: Fundamental formalism
• Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics
• Discrete and continuous boundary problems
• On the trigonometric moment problem
• ANTIBOUND STATES AND EXPONENTIALLY DECAYING STURM–LIOUVILLE POTENTIALS
• Oscillation of Eigenfunctions of Weighted Regular Sturm-Liouville Problems
• On the location of the Weyl circles
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Schur's algorithm, orthogonal polynomials, and convergence of Wall's continued fractions in \(L^2(\mathbb{T})\).
• Szegö difference equations, transfer matrices and orthogonal polynomials on the unit circle