Doubly infinite Jacobi matrices revisited: resolvent and spectral measure

DOI10.1016/j.aim.2018.11.017OpenAlexW2903458321MaRDI QIDQ1711910

Dan Dai, Mourad E. H. Ismail, Xiang-Sheng Wang

Publication date: 18 January 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2018.11.017

zbMATH Keywords

spectral analysisLommel polynomialsdoubly infinite Jacobi matrixAl-Salam-Ismail polynomialsassociated ultraspherical polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (6)

L-matrices with lacunary coefficients ⋮ The bilateral birth–death chain generated by the associated Jacobi polynomials ⋮ The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers ⋮ Characteristic polynomials of random banded Hessenberg matrices and Hermite-Padé approximation ⋮ Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformations ⋮ The norm of an infinite L-matrix

Uses Software

• DLMF

Cites Work

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• A hypergeometric function transform and matrix-valued orthogonal polynomials
• Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction
• The Nevanlinna parametrization for \(q\)-Lommel polynomials in the indeterminate case
• Linear birth and death models and associated Laguerre and Meixner polynomials
• Ratio asymptotics for orthogonal matrix polynomials
• Associated Wilson polynomials
• A survey on orthogonal matrix polynomials satisfying second order differential equations
• Zero asymptotic behaviour for orthogonal matrix polynomials
• Spectral decomposition and matrix-valued orthogonal polynomials
• Wilson function transforms related to Racah coefficients
• A class of continued fractions
• Associated Laguerre and Hermite polynomials
• Spectral Theory of Jacobi Matrices in $l^2 (\mathbb{Z})$ and the $su(1,1)$ Lie Algebra
• The Analytic Theory of Matrix Orthogonal Polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• The Associated Askey-Wilson Polynomials
• Chain Sequences and Orthogonal Polynomials
• On Constructing Distribution Functions; with Applications to Lommel Polynomials and Bessel Functions

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