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

共 50 条

[11] COMPOSITION OPERATORS ON DIRICHLET-TYPE SPACES
Yang, Liu
Shi, Yecheng
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2017, 23 (02) : 229 - 238
[12] A new formalization of Dirichlet-type spaces
Balooch, Ali
Wu, Zhijian
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 526 (01)
[13] Univalent Functions in Dirichlet-Type Spaces
Qian, Ruishen
Shi, Yecheng
[J]. FILOMAT, 2016, 30 (05) : 1213 - 1218
[14] The backward shift on Dirichlet-type spaces
Garcia, SR
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (10) : 3047 - 3056
[15] ON THE ZEROS OF FUNCTIONS IN DIRICHLET-TYPE SPACES
Pau, Jordi
Angel Pelaez, Jose
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (04) : 1981 - 2002
[16] Generalized Cesaro Operators on Dirichlet-Type Spaces
Jin, Jianjun
Tang, Shuan
[J]. ACTA MATHEMATICA SCIENTIA, 2021, 42 (1) : 212 - 220
[17] CARLESON MEASURES AND MULTIPLIERS OF DIRICHLET-TYPE SPACES
KERMAN, R
SAWYER, E
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 309 (01) : 87 - 98
[18] Radial variation of functions in Dirichlet-type spaces
Twomey, JB
[J]. MATHEMATIKA, 1997, 44 (88) : 267 - 277
[19] GENERALIZED CESàRO OPERATORS ON DIRICHLET-TYPE SPACES
金建军
唐树安
[J]. Acta Mathematica Scientia, 2022, (01) : 212 - 220
[20] Lacunary Series in Dirichlet-Type Spaces and Pseudoanalytic Extension
Ruishen Qian
Songxiao Li
[J]. Computational Methods and Function Theory, 2018, 18 : 409 - 425

← 1 2 3 4 5 →