Doubly infinite Jacobi matrices revisited : Resolvent and spectral measure

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-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
Early online date27 Nov 2018
StatePublished - 5 Feb 2019

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

Citation Format(s)

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, 22, 62)21_Publication in refereed journalNot applicablepeer-review