Orthogonal polynomials and perturbations on measures supported on the real line and on the unit circle. A matrix perspective
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Publication:530364
DOI10.1016/j.exmath.2015.12.007zbMath1342.42026OpenAlexW2289231595MaRDI QIDQ530364
Francisco Marcellán, Luis E. Garza
Publication date: 29 July 2016
Published in: Expositiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.exmath.2015.12.007
orthogonal polynomialsintegrable systemsJacobi matricesCMV matricesspectral transformationsSzego transformation
Factorization of matrices (15A23) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Applications of Lie algebras and superalgebras to integrable systems (17B80)
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- Equations of motion for zeros of orthogonal polynomials related to the Toda lattices
- Perturbations on the subdiagonals of Toeplitz matrices
- Spectral transformations for Hermitian Toeplitz matrices
- Orthogonal polynomials with respect to the sum of an arbitrary measure and a Bernstein-Szegö measure
- On perturbed Szegő recurrences
- Perturbations on the antidiagonals of Hankel matrices
- On co-polynomials on the real line
- Spectral transformations of measures supported on the unit circle and the Szegő transformation
- Orthogonal polynomials and measures on the unit circle. The geronimus transformations
- Orthogonal polynomials and measures with end point masses
- Relation between polynomials orthogonal on the unit circle with respect to different weights
- Finite perturbations of orthogonal polynomials
- On the assignment of a Dirac-mass for a regular and semi-classical form
- Theory of nonlinear lattices.
- Three integrable Hamiltonian systems connected with isospectral deformations
- The spectrum of Hill's equation
- The spectrum of Jacobi matrices
- WKB approximation and Krall-type orthogonal polynomials
- Lebesgue perturbation of a quasi-definite Hermitian functional. The positive definite case
- An electrostatics model for zeros of general orthogonal polynomials
- Darboux transformation and perturbation of linear functionals
- Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
- A special class of polynomials orthogonal on the unit circle including the associated polynomials
- Christoffel transforms and Hermitian linear functionals
- Some Perspectives on the Eigenvalue Problem
- On a Direct Uvarov-Chihara Problem and Some Extensions
- Schur flows and orthogonal polynomials on the unit circle
- Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
- An integrable system connected with the Uvarov-Chihara problem for orthogonal polynomials
- Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
- Spectral transformations, self-similar reductions and orthogonal polynomials
- Ladder operators and differential equations for orthogonal polynomials
- Orthogonal Polynomials and Rational Modifications of Measures
- More on Electrostatic Models for Zeros of Orthagonal Polynomials
- DARBOUX TRANSFORMS AND ORTHOGONAL POLYNOMIALS
- The connection between systems of polynomials orthogonal with respect to different distribution functions
- Discriminants and functional equations for polynomials orthogonal on the unit circle
- Schur flow for orthogonal polynomials on the unit circle and its integrable discretization