Doubly infinite Jacobi matrices revisited : Resolvent and spectral measure

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Author(s)

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

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)157-192
Journal / PublicationAdvances in Mathematics
Volume343
Online published27 Nov 2018
Publication statusPublished - 5 Feb 2019

Link(s)

DOI

DOI
Check@CityULib
Link to Scopus https://www.scopus.com/record/display.uri?eid=2-s2.0-85057287054&origin=recordpage
Permanent Link https://scholars.cityu.edu.hk/en/publications/publication(a078cdec-0514-4ffc-a6dd-52791a0138d2).html

Abstract

We study the resolvent and spectral measure of certain doubly infinite Jacobi matrices via asymptotic solutions of two-sided difference equations. By finding the minimal (or subdominant) solutions or calculating the continued fractions for the difference equations, we derive explicit formulas for the matrix entries of resolvent of doubly infinite Jacobi matrices corresponding to Lommel polynomials, associated ultraspherical polynomials, and Al-Salam–Ismail polynomials. The spectral measures are then obtained by inverting Stieltjes transformations.

Research Area(s)

  • Al-Salam–Ismail polynomials, Associated ultraspherical polynomials, Doubly infinite Jacobi matrix, Lommel polynomials, Spectral analysis

Fingerprint

Publication fingerprints text

100
Polynomial Mathematics
100
Jacobi Matrix Mathematics
100
Resolvent Mathematics
66
Difference Equation Mathematics
33
Matrix (Mathematics... Mathematics
33
Asymptotics Mathematics
33
Stieltjes Mathematics
33
Explicit Formula Mathematics
33
Continued Fraction Mathematics
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Citation Format(s)

[ RIS ] [ BibTeX ]
Doubly infinite Jacobi matrices revisited: Resolvent and spectral measure. / Dai, Dan; Ismail, Mourad E.H.; Wang, Xiang-Sheng.
In: Advances in Mathematics, Vol. 343, 05.02.2019, p. 157-192.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review