The Analytic Theory of Matrix Orthogonal Polynomials

From MaRDI portal
Publication:3406473

zbMath1193.42097arXiv0711.2703MaRDI QIDQ3406473

Alexander Pushnitski, Barry Simon, David Damanik

Publication date: 16 February 2010

Full work available at URL: https://arxiv.org/abs/0711.2703




Related Items (only showing first 100 items - show all)

Asymptotics of matrix valued orthogonal polynomials on \([-1, 1\)] ⋮ Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomialsExplicit relation between two resolvent matrices of the truncated Hausdorff matrix moment problemSpectral measure of empirical autocovariance matrices of high-dimensional Gaussian stationary processesDuality and difference operators for matrix valued discrete polynomials on the nonnegative integersOn the Hahn's property for matrix orthogonal polynomials on the unit circleNon-Abelian Toda-type equations and matrix valued orthogonal polynomialsCoefficient stripping in the matricial Nehari problemDiscrete self-adjoint Dirac systems: asymptotic relations, Weyl functions and Toeplitz matricesSpectral properties of block Jacobi matricesOn the instability of the essential spectrum for block Jacobi matricesMatrix-valued orthogonal polynomials related to hexagon tilingsApplication of matrix-valued integral continued fractions to spectral problems on periodic graphs with defectsLarge deviations for spectral measures of some spiked matricesRiemann-Hilbert Problems, Matrix Orthogonal Polynomials and Discrete Matrix Equations with Singularity ConfinementPrediction theory for stationary functional time seriesThree-term recurrence relation coefficients and continued fractions related to orthogonal matrix polynomials on the finite interval [a, b] ⋮ An extension of the Geronimus transformation for orthogonal matrix polynomials on the real lineRelative asymptotics of matrix orthogonal polynomials for Uvarov perturbations: the degenerate caseMatrix-valued orthogonal polynomials related to \((\mathrm{SU}(2) \times \mathrm{SU}(2), \mathrm{diag})\). IIZeros and ratio asymptotics for matrix orthogonal polynomialsOn the Szegő transformation for some spectral perturbations of matrix measuresThe resolvent matrix for the Hausdorff matrix moment problem expressed in terms of orthogonal matrix polynomialsSpectra of Jacobi operators via connection coefficient matricesCMV block matrices for symmetric matrix measures on the unit circleMatrix-valued orthogonal polynomials related to the quantum analogue of \((\mathrm{SU}(2) \times \mathrm{SU}(2), \text{diag})\)Vector interpretation of the matrix orthogonality on the real lineNon-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbationsKillip-Simon problem and Jacobi flow on GMP matricesThe matrix Bochner problemMatrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systemsUni-asymptotic linear systems and Jacobi operatorsMatrix-valued Gegenbauer-type polynomialsA generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walksDyukarev-Stieltjes parameters of the truncated Hausdorff matrix moment problemMatrix measures, random moments, and Gaussian ensemblesScattering zippers and their spectral theoryRelations between the orthogonal matrix polynomials on \([a,b\), Dyukarev-Stieltjes parameters, and Schur complements] ⋮ Spectral methods for bivariate Markov processes with diffusion and discrete components and a variant of the Wright-Fisher modelMatrix orthogonal polynomials associated with perturbations of block Toeplitz matricesOrthogonal vs. non-orthogonal reducibility of matrix-valued measuresMultivariate prediction and matrix Szegő theorySpectral decomposition and matrix-valued orthogonal polynomialsSum rules and large deviations for spectral measures on the unit circleRelative asymptotics for orthogonal matrix polynomialsNon-commutative Painlevé equations and Hermite-type matrix orthogonal polynomialsDoubly infinite Jacobi matrices revisited: resolvent and spectral measureSum rules and large deviations for spectral matrix measuresOperator-valued spectral measures and large deviationsThe zeros of determinants of matrix-valued polynomials that are orthonormal on a semi-infinite or finite intervalMeromorphic continuations of finite gap Herglotz functions and periodic Jacobi matricesDualities in the q‐Askey Scheme and Degenerate DAHAOrthogonal polynomials associated with some Jacobi-type pencilsJacobi operators and orthonormal matrix-valued polynomials. IJacobi operators and orthonormal matrix-valued polynomials. IIMatrix Uvarov transformation on the unit circle: asymptotic propertiesTwo Variable Orthogonal Polynomials and Fejér-Riesz FactorizationFrom the Potapov to the Krein-Nudel'man representation of the resolvent matrix of the truncated Hausdorff matrix moment problemOn Conditions of Complete Indeterminacy for the Matricial Hamburger Moment ProblemA canonical Geronimus transformation for matrix orthogonal polynomialsHalf line Titchmarsh-Weyl \(m\) functions of vector-valued discrete Schrödinger operatorsHyponormal Toeplitz operators on weighted Bergman spacesElementary examples of solutions to Bochner's problem for matrix differential operatorsQuantum recurrence of a subspace and operator-valued Schur functionsThe CGMV method for quantum walksSpectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuumSome examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctionsThe maximization of determinants of block Toeplitz matrices with applications in optimal design theoryAbsence of absolutely continuous spectrum for random scattering zippersPerturbations of orthogonal polynomials with periodic recursion coefficientsGeometry of Weyl theory for Jacobi matrices with matrix entriesMatrix measures on the unit circle, moment spaces, orthogonal polynomials and the Geronimus relationsSzegő asymptotics for matrix-valued measures with countably many bound statesRandom block matrices generalizing the classical Jacobi and Laguerre ensemblesTrace formulas and a Borg‐type theorem for CMV operators with matrix‐valued coefficientsSzegő's theorem for matrix orthogonal polynomialsJost asymptotics for matrix orthogonal polynomials on the real lineMatrix-valued SzegoÌ polynomials and quantum random walksChristoffel transformation for a matrix of bi-variate measuresDeterminants of block Hankel matrices for random matrix-valued measuresA matrix version of a higher-order Szegő theoremThe two-periodic Aztec diamond and matrix valued orthogonal polynomialsCMV matrices, a matrix version of Baxter's theorem, scattering and de Branges spacesGreen matrix estimates of block Jacobi matrices. I: Unbounded gap in the essential spectrumMatrix elements of irreducible representations of \(\mathrm{GL} (n + 1) \times\mathrm{GL} (n + 1)\) and multivariable matrix-valued orthogonal polynomialsSpectral theory of a class of block Jacobi matrices and applicationsA Quantum Dynamical Approach to Matrix Khrushchev's FormulasMatrix polynomials orthogonal with respect to a non-symmetric matrix of measuresNew ``Verblunsky-type coefficients of block Toeplitz and Hankel matrices and of corresponding Dirac and canonical systemsRegularity and the Cesàro-Nevai classOn a Christoffel transformation for matrix measures supported on the unit circleThe matrix Toda equations for coefficients of a matrix three-term recurrence relationEquivalence classes of block Jacobi matricesBlock Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circleThe Kähler Mean of Block-Toeplitz Matrices with Toeplitz Structured BlocksLarge deviations for random matricial moment problemsQuantum walks: Schur functions meet symmetry protected topological phasesRatio asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficientsMatrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda latticeMatrix biorthogonal polynomials on the real line: Geronimus transformations




This page was built for publication: The Analytic Theory of Matrix Orthogonal Polynomials