Interlacing properties of zeros of multiple orthogonal polynomials

DOI10.1016/j.jmaa.2011.11.077zbMath1235.33007arXiv1108.3917OpenAlexW2155026701MaRDI QIDQ663718

Maciej Haneczok, Walter Van Assche

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.3917

zbMATH Keywords

recurrence relationsmultiple orthogonal polynomialsinterlacing zeros

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (16)

The symmetrization problem for multiple orthogonal polynomials ⋮ Mixed type multiple orthogonal polynomials: Perfectness and interlacing properties of zeros ⋮ On connection between zeros and d -orthogonality ⋮ Asymptotics for the ratio and the zeros of multiple Charlier polynomials ⋮ Asymptotics for the ratio and the zeros of multiple Charlier polynomials ⋮ Solutions of convex Bethe ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials ⋮ Multiple q-Kravchuk polynomials ⋮ Spectral curves, variational problems and the Hermitian matrix model with external source ⋮ Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials ⋮ On the zeros of $d$-orthogonal Laguerre polynomials and their $q$-analogues ⋮ Global fluctuations for multiple orthogonal polynomial ensembles ⋮ Spectral theory of Jacobi matrices on trees whose coefficients are generated by multiple orthogonality ⋮ Multiple orthogonal polynomials: Pearson equations and Christoffel formulas ⋮ Christoffel functions for multiple orthogonal polynomials ⋮ On the zeros of some d-orthogonal polynomials ⋮ Asymptotic zero distribution of Jacobi-Piñeiro and multiple Laguerre polynomials

Cites Work

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• Hermite--Padé approximation and simultaneous quadrature formulas
• Nearest neighbor recurrence relations for multiple orthogonal polynomials
• The zeros of Faber polynomials for an \(m\)-cusped hypocycloid
• Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains
• The genetic sums' representation for the moments of a system of Stieltjes functions and its application
• A Note on Extended Gaussian Quadrature Rule
• The Zeros of Special Functions from a Fixed Point Method
• A note on orthogonal polynomials
• Ratio asymptotics of Hermite-Padé polynomials for Nikishin systems
• Mixed type multiple orthogonal polynomials for two Nikishin systems

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