The Analytic Theory of Matrix Orthogonal Polynomials
arXiv:0711.2703
Abstract
We give a survey of the analytic theory of matrix orthogonal polynomials.
85 pages
References in corpus (3)
Cited by in corpus (46)
- Quantum recurrence of a subspace and operator-valued Schur functions
- Matrix Orthogonal Laurent Polynomials on the Unit Circle and Toda Type Integrable Systems
- Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization
- Riemann--Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement
- Matrix Valued Classical Pairs Related to Compact Gelfand Pairs of Rank One
- Quantum walks: Schur functions meet symmetry protected topological phases
- Dualities in the -Askey scheme and degenerate DAHA
- Orthogonal vs. Non-Orthogonal Reducibility of Matrix-Valued Measures
- A quantum dynamical approach to matrix Khrushchev's formulas
- Transformation theory and Christoffel formulas for matrix biorthogonal polynomials on the real line
- Szegő's theorem for matrix orthogonal polynomials
- Spectral properties of block Jacobi matrices
- The Matrix Bochner Problem
- Representations of the Schrödinger group and matrix orthogonal polynomials
- Ladder relations for a class of matrix valued orthogonal polynomials
- Verblunsky-type coefficients for Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively
- One-dimensional quantum walks with one defect
- Szego asymptotics for matrix-valued measures with countably many bound states
- Multivariate prediction and matrix Szegö theory
- Baxter's inequality for finite predictor coefficients of multivariate long-memory stationary processes
- Matrix biorthogonal polynomials in the unit circle: Riemann-Hilbert problem and matrix discrete Painleve II system
- Minimal Rank Decoupling of Full-Lattice CMV Operators with Scalar- and Matrix-Valued Verblunsky Coefficients
- Matrix valued Szego polynomials and quantum random walks
- Matrix measures, random moments and Gaussian ensembles
- Spectral and resonance problem for perturbations of periodic Jacobi operators
- Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation
- Hyponormal Toeplitz Operators on Weighted Bergman Spaces
- Matrix elements of irreducible representations of and multivariable matrix-valued orthogonal polynomials
- Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble
- A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks
- Sum rules and large deviations for spectral measures on the unit circle
- A class of matrix-valued polynomials generalizing Jacobi Polynomials
- Large Deviations for Random Matricial Moment Problems
- Titchmarsh-Weyl theory for vector valued Schrodinger operators
- Matrix-Valued Little q-Jacobi Polynomials
- Matrix measures on the unit circle, moment spaces, orthogonal polynomials and the Geronimus relations
- Ratio asymptotic for bi-orthogonal matrix polynomials with unbounded recurrence coefficients
- Zeros and ratio asymptotics for matrix orthogonal polynomials
- Regularity and the Cesaro-Nevai class
- Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients
- Matrix valued polynomials generated by the scalar-type Rodrigues' formulas
- Spectral measure of empirical autocovariance matrices of high dimensional Gaussian stationary processes
- Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions
- Equivalence classes of block Jacobi matrices
- Absence of absolutely continuous spectrum for random scattering zippers
- Application of matrix-valued integral continued fractions to spectral problems on periodic graphs