Orthogonal polynomials for the weakly equilibrium cantor sets
Date
2016
Authors
Alpan, G.
Goncharov, A.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Proceedings of the American Mathematical Society
Print ISSN
0002-9939
Electronic ISSN
1088-6826
Publisher
American Mathematical Society
Volume
144
Issue
9
Pages
3781 - 3795
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Series
Abstract
Let K(γ) be the weakly equilibrium Cantor-type set introduced by the second author in an earlier work. It is proven that the monic orthogonal polynomials Q2 s with respect to the equilibrium measure of K(γ) coincide with the Chebyshev polynomials of the set. Procedures are suggested to find Qn of all degrees and the corresponding Jacobi parameters. It is shown that the sequence of the Widom factors is bounded below. © 2016 American Mathematical Society.