Projects per year
Abstract
In this paper we study the sequence of orthonormal polynomials {Pn(μ;z)} defined by a Borel probability measure μ with nonpolar compact support S(μ)⊂C. For each n ≥ 2 let ωn denote the unique measure of maximal entropy for Pn(μ;z). We prove that the sequence {ωn}n is precompact for the weak* topology and that for any weak* limit ν of a convergent subsequence {ωnk}, the support S(ν) is contained in the filledin or polynomialconvex hull of the support S(μ) for μ. And for nth root regular measures μ the full sequence {ωn}n converges weak* to the equilibrium measure ω on S(μ).
Translated title of the contribution  Om svage grænser af målene med maksimal entropi for orthogonale polynomier 

Original language  English 
Journal  Potential Analysis 
Volume  2020 
Issue number  54 
Pages (fromto)  219225 
Number of pages  7 
ISSN  09262601 
DOIs  
Publication status  Published  2021 
Projects
 1 Finished

Holomorpic Dynamics and Orthogonal Polynomials
Petersen, C. L., Petersen, H. L., Henriksen, C. & Christiansen, J. S.
01/11/2015 → 31/10/2018
Project: Research