Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems

被引：12

作者：

Beneteau, Catherine ^{[1
]}

Khavinson, Dmitry ^{[1
]}

Liaw, Constanze ^{[2
]}

Seco, Daniel ^{[3
,4
]}

Simanek, Brian ^{[5
]}

机构：

[1] Univ S Florida, Dept Math, 4202 E Fowler Ave, Tampa, FL 33620 USA

[2] Univ Delaware, Dept Math Sci, 311 Ewing Hall, Newark, DE 19716 USA

[3] Univ Carlos III Madrid, Ave Univ 30, Leganes 28911, Madrid, Spain

[4] Inst Ciencias Matemat ICMAT, Dept Matemat UC3M, Ave Univ 30, Leganes 28911, Madrid, Spain

[5] Baylor Univ, Dept Math, One Bear Pl 97328, Waco, TX 76798 USA

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2019年 / 35卷 / 02期

基金：

美国国家科学基金会;

关键词：

Bergman spaces; Dirichlet spaces; cyclic functions; orthogonal polynomials;

D O I：

10.4171/RMI/1064

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the structure of the zeros of optimal polynomial approximants to reciprocals of functions in Hilbert spaces of analytic functions in the unit disk. In many instances, we find the minimum possible modulus of occurring zeros via a nonlinear extremal problem associated with norms of Jacobi matrices. We examine global properties of these zeros and prove Jentzsch-type theorems describing where they accumulate. As a consequence, we obtain detailed information regarding zeros of reproducing kernels in weighted spaces of analytic functions.

引用

页码：607 / 642

页数：36

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