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  54 
Issue number  2 
Pages (fromto)  219225 
Number of pages  7 
ISSN  09262601 
DOIs  
Publication status  Published  Feb 2021 
Bibliographical note
Important note from the Publisher regarding te attached version of the article: “This is a postpeerreview, precopyedit version of an article published in Potential Analysis. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11118019098245”.Keywords
 Green’s function  Equilibriums measure
 Julia set
 Orthogonal polynomials
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