Szego's condition on compact subsets of C

JOURNAL OF APPROXIMATION THEORY

卷:245

Article

Alpan, Gokalp¹ 

[1] Rice Univ, Dept Math, Houston, TX 77005 USA

关键词: Szego condition;    widom condition;    orthogonal polynomials;    Parreau-Widom domain;   

DOI  :  10.1016/j.jat.2019.05.002

来源: Elsevier

【 摘 要 】

Let K be a non-polar compact subset of C and mu(K) be its equilibrium measure. Let mu be a unit Borel measure supported on K. We prove that a Szego condition in terms of the Radon-Nikodym derivative of mu with respect to mu(K )implies that inf(n) parallel to P-n(.; mu)(L2(C;mu))/Cap(K)(n)( )> 0.( ) We show that parallel to P-n(.; mu(K))(L2(C; mu K))/Cap(K)(n )>= 1 for any compact non-polar set K. We also prove that under an additional assumption, boundedness of the sequence (parallel to P-n(.; mu(K))(L2(C;mu K))/Cap(K)(n)) implies that K satisfies the Parreau-Widom condition. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free