Asymptotic Properties of Jacobi Matrices for a Family of Fractal Measures. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Alpan, Gökalp; Goncharov, Alexander; Şimşek, Ahmet Nihat
• Is Part Of: Experimental mathematics. Volume 27:Issue 1(2018)
• Page Start: 10
• Page End: 21
• Publication Date: 2018-01-02
• Subjects: Cantor sets -- Parreau–Widom sets -- orthogonal polynomials -- zero spacing -- Widom factors; 37F10 -- 42C05 -- 30C85; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2016.1209710
• Languages: English
• ISSNs: 1058-6458

Abstract

ABSTRACT: We study the properties and asymptotics of the Jacobi matrices associated with equilibrium measures of the weakly equilibrium Cantor sets. These family of Cantor sets were defined, and different aspects of orthogonal polynomials on them were studied recently. Our main aim is to numerically examine some conjectures concerning orthogonal polynomials which do not directly follow from previous results. We also compare our results with more general conjectures made for recurrence coefficients associated with fractal measures supported on .