CYCLICITY IN DIRICHLET-TYPE SPACES AND EXTREMAL POLYNOMIALS

被引：16

作者：

Beneteau, Catherine ^{[1
]}

Condori, Alberto A. ^{[2
]}

Liaw, Constanze ^{[3
]}

Seco, Daniel ^{[4
]}

Sola, Alan A. ^{[5
]}

机构：

[1] Univ S Florida, Dept Math, Tampa, FL 33620 USA

[2] Florida Gulf Coast Univ, Dept Math, Ft Myers, FL 33965 USA

[3] Baylor Univ, Dept Math, Waco, TX 76798 USA

[4] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain

[5] Univ Cambridge, Ctr Math Sci, Stat Lab, Cambridge CB3 0WB, England

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2015年 / 126卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

VECTORS;

D O I：

10.1007/s11854-015-0017-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For functions f in Dirichlet-type spaces D-alpha, we study how to determine constructively optimal polynomials p(n) that minimize parallel to pf - 1 parallel to(alpha) among all polynomials p of degree at most n. We then obtain sharp estimates for the rate of decay of parallel to p(n)f - 1 parallel to(alpha) as n approaches infinity, for certain classes of functions f. Finally, inspired by the Brown-Shields conjecture, we prove that certain logarithmic conditions on f imply cyclicity, and we study some computational phenomena pertaining to the zeros of optimal polynomials.

引用

页码：259 / 286

页数：28

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