Nikishin systems are perfect

DOI10.1007/s00365-011-9139-6zbMath1258.30015arXiv1001.0554OpenAlexW2099763915MaRDI QIDQ662811

Juan-Miguel Gracia

Publication date: 13 February 2012

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.0554

zbMATH Keywords

orthogonal polynomialsNikishin systemsperfect systems

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximation in the complex plane (30E10) Approximation by rational functions (41A20)

Related Items (42)

Multiple orthogonal polynomials applied to matrix function evaluation ⋮ Multidimensional Toda lattices: continuous and discrete time ⋮ High-order three-term recursions, Riemann-Hilbert minors and Nikishin systems on star-like sets ⋮ An extension of Markov’s Theorem ⋮ Convergent interpolatory quadrature schemes ⋮ Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matrices ⋮ Direct and inverse results on row sequences of Hermite-Padé approximants ⋮ An introduction to multiple orthogonal polynomials and Hermite-Padé approximation ⋮ Mixed type multiple orthogonal polynomials: Perfectness and interlacing properties of zeros ⋮ Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation ⋮ Nikishin systems on star-like sets: ratio asymptotics of the associated multiple orthogonal polynomials ⋮ Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight ⋮ Zero distribution of incomplete Padé and Hermite-Padé approximations ⋮ Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials ⋮ Multiple orthogonal polynomials with respect to Gauss' hypergeometric function ⋮ Multiple orthogonal polynomials associated with the exponential integral ⋮ On the convergence of multi-level Hermite-Padé approximants for a class of meromorphic functions ⋮ Hermite-Padé Approximants for a Pair of Cauchy Transforms with Overlapping Symmetric Supports ⋮ Multiple orthogonal polynomials associated with confluent hypergeometric functions ⋮ Mixed type Hermite-Padé approximants for a Nikishin system ⋮ Distribution of zeros of the Hermite-Padé polynomials for a system of three functions, and the Nuttall condenser ⋮ Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations ⋮ On an example of the Nikishin system ⋮ On matrix Cauchy biorthogonal polynomials ⋮ On the convergence of type I Hermite-Padé approximants ⋮ On \(L_p\) multiple orthogonal polynomials ⋮ Nikishin systems are perfect. The case of unbounded and touching supports ⋮ Riemann-Hilbert analysis for a Nikishin system ⋮ Nikishin systems on star-like sets: algebraic properties and weak asymptotics of the associated multiple orthogonal polynomials ⋮ A canonical family of multiple orthogonal polynomials for Nikishin systems ⋮ Nikishin systems on star-like sets: ratio asymptotics of the associated multiple orthogonal polynomials. II ⋮ A Jacobi type Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type ⋮ Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials ⋮ Parameters of a positive chain sequence associated with orthogonal polynomials ⋮ Unnamed Item ⋮ Spectral theory of Jacobi matrices on trees whose coefficients are generated by multiple orthogonality ⋮ A family of Nikishin systems with periodic recurrence coefficients ⋮ Christoffel functions for multiple orthogonal polynomials ⋮ Multiple orthogonal polynomials on the unit circle. Normality and recurrence relations ⋮ On the convergence of type I Hermite-Padé approximants for rational perturbations of a Nikishin system ⋮ On multiple extremal problems ⋮ Strong asymptotic of Cauchy biorthogonal polynomials and orthogonal polynomials with varying measure

Cites Work

• Hermite--Padé approximation and simultaneous quadrature formulas
• General results on the convergence of multipoint Hermite-Padé approximants of Nikishin systems
• Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions
• Ratio asymptotic of Hermite-Padé orthogonal polynomials for Nikishin systems. II
• Asymptotics of diagonal Hermite-Padé polynomials
• On a class of Gauss-like quadrature rules
• Normality in Nikishin systems
• Normal indices in Nikishin systems.
• On perfect Nikishin systems
• Best uniform rational approximation of \(x^ \alpha\) on \([0,1\).]
• Asymptotics for Angelesco-Nikishin systems
• Rate of convergence of generalized Hermite-Padé approximants of Nikishin systems
• Multiple orthogonal polynomials in random matrix theory
• Multiple orthogonal polynomial ensembles
• EQUILIBRIUM DISTRIBUTIONS AND DEGREE OF RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS
• HERMITE-PADÉ APPROXIMATION FOR NIKISHIN SYSTEMS OF ANALYTIC FUNCTIONS
• Hermite-Pade approximants for systems of Markov-type functions
• On Rakhmanov’s theorem for Jacobi matrices
• Strong asymptotics of multiply orthogonal polynomials for Nikishin systems
• Sharp constants for rational approximations of analytic functions
• Mixed type multiple orthogonal polynomials for two Nikishin systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Nikishin systems are perfect